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We report on INTEGRAL observations of the bright black-hole transient GX 339-4 performed during the period August-September 2004. Our data cover three different spectral states, namely Hard/Intermediate State, Soft/Intermediate State and High/Soft State. We investigate the spectral variability of the source across the different spectral states. The hard X-ray spectrum becomes softer during the HIMS-to-SIMS transition, but it hardens when reaching the HSS state. A principal component analysis demonstrates that most of the variability occurs through two independent modes: a pivoting of the spectrum around 6 keV (responsible for 75% of the variance) and an intensity variation of the hard component (responsible for 21%). The pivoting is interpreted as due to changes in the soft cooling photon flux entering the corona, the second mode as fluctuations of the heating rate in the corona. Our spectral analysis of the spectra of GX 339-4 shows a high energy excess with respect to pure thermal Comptonisation models in the HIMS: a non-thermal power-law component seems to be requested by data. In all spectral states joint IBIS, SPI and JEM-X data are well represented by hybrid thermal/non-thermal Comptonisation (EQPAIR). The spectral evolution seems to be predominantly driven by a reduction of the ratio of the electron heating rate to the soft cooling photon flux in the corona, l_h/l_s. The inferred accretion disc soft thermal emission increases by about two orders of magnitude, while the Comptonised luminosity decreases by at most a factor of 3. This confirms that the softening we observed is due to a major increase in the flux of soft cooling photons in the corona associated with a modest reduction of the electron heating rate., Comment: 11 pages, 6 figures, 4 tables; accepted for publication in MNRAS Main Journal

We have processed the data accumulated with INTEGRAL SPI during 4 years (~ 51 Ms) to study the Galactic ``diffuse'' emission morphology in the 20 keV to 8 MeV energy range. To achieve this objective, we have derived simultaneously an all-sky census of emitting sources and images of the Galactic Ridge (GR) emission. In the central radian, the resolved point source emission amounts to 88%, 91% and 68% of the total emission in the 25-50, 50-100 and 100-300 keV domains respectively. We have compared the GR emission spatial distribution to those obtained from CO and NIR maps, and quantified our results through latitude and longitude profiles. Below 50 keV, the SPI data are better traced by the latter, supporting a stellar origin for this emission. Furthermore, we found that the GR emission spectrum follows a power law with a photon index ~ 1.55 above 50 keV while an additional component is required below this energy. This component shows a cutoff around 30 keV, reinforcing a stellar origin, as proposed by Krivonos et al. (2007). The annihilation diffuse emission component is extracted simultaneously, leading to the determination of the related parameters (positronium flux and fraction). A specific discussion is devoted to the annihilation line distribution since a significant emission is detected over a region as large as ~80 degrees by ~10 degrees potentially associated with the disk or halo surrounding the central regions of our Galaxy., Comment: 28 pages, 10 figures. Astrophysical journal (accepted for publication)

In this paper, we propose a stratified sampling algorithm in which the random drawings made in the strata to compute the expectation of interest are also used to adaptively modify the proportion of further drawings in each stratum. These proportions converge to the optimal allocation in terms of variance reduction. And our stratified estimator is asymptotically normal with asymptotic variance equal to the minimal one. Numerical experiments confirm the efficiency of our algorithm.

In this paper we study general nonlinear stochastic differential equations, where the usual Brownian motion is replaced by a L\'evy process. We also suppose that the coefficient multiplying the increments of this process is merely Lipschitz continuous and not necessarily linear in the time-marginals of the solution as is the case in the classical McKean-Vlasov model. We first study existence, uniqueness and particle approximations for these stochastic differential equations. When the driving process is a pure jump L\'evy process with a smooth but unbounded L\'evy measure, we develop a stochastic calculus of variations to prove that the time-marginals of the solutions are absolutely continuous with respect to the Lebesgue measure. In the case of a symmetric stable driving process, we deduce the existence of a function solution to a nonlinear integro-differential equation involving the fractional Laplacian.

Taking advantage of the recent litterature on exact simulation algorithms (Beskos, Papaspiliopoulos and Roberts) and unbiased estimation of the expectation of certain fonctional integrals (Wagner, Beskos et al. and Fearnhead et al.), we apply an exact simulation based technique for pricing continuous arithmetic average Asian options in the Black and Scholes framework. Unlike existing Monte Carlo methods, we are no longer prone to the discretization bias resulting from the approximation of continuous time processes through discrete sampling. Numerical results of simulation studies are presented and variance reduction problems are considered.

The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a {\bf fixed} number of random walkers evolving according to a Stochastic Differential Equation discretized in time. We allow stochastic reconfigurations of the walkers to reduce the discrepancy between the weights that they carry. On a simple one-dimensional example, we prove the convergence of the method for a fixed number of reconfigurations when the number of walkers tends to $+\infty$ while the timestep tends to 0. We confirm our theoretical rates of convergence by numerical experiments. Various resampling algorithms are investigated, both theoretically and numerically

In the particular case of a concave flux function, we are interested in the long time behaviour of the nonlinear process associated to the one-dimensional viscous scalar conservation law. We also consider the particle system obtained by remplacing the cumulative distribution function in the drift coefficient of this nonlinear process by the empirical cdf. We first obtain trajectorial propagation of chaos result. Then, Poincar\'e inequalities are used to get explicit estimates concerning the long time behaviour of both the nonlinear process and the particle system.

In this paper, we investigate the generalization of the Call-Put duality equality obtained in [1] for perpetual American options when the Call-Put payoff $(y-x)^+$ is replaced by $\phi(x,y)$. It turns out that the duality still holds under monotonicity and concavity assumptions on $\phi$. The specific analytical form of the Call-Put payoff only makes calculations easier but is not crucial unlike in the derivation of the Call-Put duality equality for European options. Last, we give some examples for which the optimal strategy is known explicitly.

It is well known that in models with time-homogeneous local volatility functions and constant interest and dividend rates, the European Put prices are transformed into European Call prices by the simultaneous exchanges of the interest and dividend rates and of the strike and spot price of the underlying. This paper investigates such a Call Put duality for perpetual American options. It turns out that the perpetual American Put price is equal to the perpetual American Call price in a model where, in addition to the previous exchanges between the spot price and the strike and between the interest and dividend rates, the local volatility function is modified. We prove that equality of the dual volatility functions only holds in the standard Black-Scholes model with constant volatility. Thanks to these duality results, we design a theoretical calibration procedure of the local volatility function from the perpetual Call and Put prices for a fixed spot price $x_0$. The knowledge of the Put (resp. Call) prices for all strikes enables to recover the local volatility function on the interval $(0,x_0)$ (resp. $(x_0,+\infty)$).

The Metropolis Hastings algorithm and its multi-proposal extensions are aimed at the computation of the expectation $<\pi,f>$ of a function $f$ under a probability measure $\pi$ difficult to simulate. They consist in constructing by an appropriate acceptation/rejection procedure a Markov chain $(X_k,k\geq 0)$ with transition matrix $P$ such that $\pi$ is reversible with respect to $P$ and in estimating $<\pi,f>$ by the empirical mean $I_n(f)=\inv{n}\sum_{k=1}^n f(X_k)$. The waste-recycling Monte Carlo (WR) algorithm introduced by physicists is a modification of the Metropolis-Hastings algorithm, which makes use of all the proposals in the empirical mean, whereas the standard Metropolis-Hastings algorithm only uses the accepted proposals. In this paper, we extend the WR algorithm into a general control variate technique and exhibit the optimal choice of the control variate in terms of asymptotic variance. We also give an example which shows that in contradiction to the intuition of physicists, the WR algorithm can have an asymptotic variance larger than the one of the Metropolis-Hastings algorithm. However, in the particular case of the Metropolis-Hastings algorithm called Boltzmann algorithm, we prove that the WR algorithm is asymptotically better than the Metropolis-Hastings algorithm.

We present the analysis of the high energy emission of the Galactic black hole binary GX 339-4 in a low/hard state at the beginning of its 2004 outburst. The data from 273 ks of INTEGRAL observations, spread over 4 weeks, are analyzed, along with the existing simultaneous RXTE HEXTE and PCA data. During this period, the flux increases by a factor of about 3, while the spectral shape is quite unchanged, at least up to 150 keV. The high energy data allows us to detect the presence of a high energy cut-off, generally related to thermal mechanisms, and to estimate the plasma parameters in the framework of the Comptonization models. We found an electron temperature of 60-70 keV, an optical depth around 2.5, with a rather low reflection factor (0.2-0.4). In the last observation, we detected a high energy excess above 200 keV with respect to thermal Comptonization while at lower energy, the spectrum is practically identical to the previous one, taken just 2 days before. This suggests that the low and high energy components have a different origin., Comment: 12 pages, 6 figures, accepted for publication in ApJ

The probabilistic equivalent formulation of Dupire's PDE is the Put-Call duality equality. In local volatility models including exponential L\'{e}vy jumps, we give a direct probabilistic proof for this result based on stochastic flows arguments. This approach also enables us to check the probabilistic equivalent formulation of various generalizations of Dupire's PDE recently obtained by Pironneau by the adjoint equation technique in the case of complex options.

We study the spectrum of the cosmic X-ray background (CXB) in energy range $\sim$5-100 keV. Early in 2006 the INTEGRAL observatory performed a series of four 30ksec observations with the Earth disk crossing the field of view of the instruments. The modulation of the aperture flux due to occultation of extragalactic objects by the Earth disk was used to obtain the spectrum of the Cosmic X-ray Background(CXB). Various sources of contamination were evaluated, including compact sources, Galactic Ridge emission, CXB reflection by the Earth atmosphere, cosmic ray induced emission by the Earth atmosphere and the Earth auroral emission. The spectrum of the cosmic X-ray background in the energy band 5-100 keV is obtained. The shape of the spectrum is consistent with that obtained previously by the HEAO-1 observatory, while the normalization is $\sim$10% higher. This difference in normalization can (at least partly) be traced to the different assumptions on the absolute flux from the Crab Nebulae. The increase relative to the earlier adopted value of the absolute flux of the CXB near the energy of maximum luminosity (20-50 keV) has direct implications for the energy release of supermassive black holes in the Universe and their growth at the epoch of the CXB origin., Comment: A&A, 14 pages, 12 figues

We extend the investigation of general relativistic effects on the observed X-ray continuum of Kerr black holes in the context of the light bending model (Miniutti & Fabian, 2004). Assuming a ring-like illuminating source, co-rotating with the underlying accretion disk, we study the shape and normalisation of the primary and disc reflected continuum as well as the dependence of the observed spectrum on the line of sight for various source heights and radii. These calculations are performed using Monte-Carlo methods to compute the angle dependent reflection spectrum from the disc. The effects of general relativity are illustrated by a comparison with Newtonian and Special Relativity calculations. We find that relativistic distortions can strongly affect the shape of the reflected spectrum. Light bending can dramatically increase the observable reflected flux and reduce the primary emission. In addition, multiple reflections due to the reflected photons deflected toward the disc can alter significantly the shape of the spectrum above 10 keV. Large variations of the ring radius at constant height can lead to an (unobserved) anti-correlation between primary and reflected flux. In another side, the variability behaviour of several sources can be reproduced if the ring source radius is small (<5 r_g), and its height varies by a large factor. In particular, a non-linear flux-flux relation, similar to that observed in several sources, can be produced. We compare our model with the flux-flux plot of NGC4051, and find an agreement for low inclination angles (<20 deg.), ring source radius <3 r_g and a height varying between 0.5 to 10 r_g., Comment: 13 pages, 18 figures. Accepted for publication in A&A

We report the results of an observation of Cygnus X-1 with INTEGRAL, that we combine with simultaneous radio observations with the Ryle telescope. Both spectral and variability properties of the source indicate that Cygnus X-1 was in an Intermediate State. The INTEGRAL spectrum shows a high-energy cut-off or break around 100 keV. The shape of this cut-off differs from pure thermal Comptonisation, suggesting the presence of a non-thermal component at higher energies.The average broad band spectrum is well represented by hybrid thermal/non-thermal Comptonisation models. During the 4 day long observation the source showed an important spectral and flux variability. A principal component analysis demonstrates that most of this variability occurs through 2 independent modes. The first mode consists in changes in the overall luminosity on time scale of hours with almost constant spectra that are strikingly uncorrelated with the variable radio flux. We interpret this variability mode as variations of the dissipation rate in the corona. The second variability mode consists in a pivoting of the spectrum around 10 keV. It acts on a longer time-scale: initially soft, the spectrum hardens in the first part of the observation and then softens again. This pivoting pattern is strongly correlated with the radio (15 GHz) emission: radio fluxes are stronger when the INTEGRAL spectrum is harder. We propose that the pivoting mode represents a 'mini' state transition from a nearly High Soft State to a nearly Low Hard State, and back. This mini-transition would be caused by changes in the soft cooling photons flux in the hot Comptonising plasma associated with an increase of the temperature of the accretion disc. The jet power then appears to be anti-correlated with the disc luminosity and unrelated to the coronal power., Comment: 14 pages, 13 figures, accepted for publication in Astronomy and Astrophysics

The INTEGRAL satellite extensively observed the black hole binary Cygnus X-1 from 2002 November to 2004 November during calibration, open time and core program (Galactic Plane Scan) observations. These data provide evidence for significant spectral variations over the period. In the framework of the accreting black hole phenomenology, the source was most of the time in the Hard State and occasionally switched to the so-called "Intermediate State". Using the results of the analysis performed on these data, we present and compare the spectral properties of the source over the whole energy range (5 keV - 1 MeV) covered by the high-energy instruments on board INTEGRAL, in both observed spectral states. Fe line and reflection component evolution occurs with spectral changes in the hard and soft components. The observed behaviour of Cygnus X-1 is consistent with the general picture of galactic black holes. Our results give clues to the physical changes that took place in the system (disc and corona) at almost constant luminosity during the spectral transitions and provide new measures of the spectral model parameters. In particular, during the Intermediate State of 2003 June, we observe in the Cygnus X-1 data a high-energy tail at several hundred keV in excess of the thermal Comptonization model which suggests the presence of an additional non-thermal component., Comment: accepted for publication in A&A, 13 pages, 9 figures (3 in colour)

IGR J17464-3213, already known as the HEAO-1 transient source H1743-322, has been detected during a state transition by the SPI/INTEGRAL telescope. We describe the spectral evolution and flaring activity of IGR J17464-3213/H1743-322 from 2003 March 21 to 2003 April 22. During the first part, the source followed a continuous spectral softening, with the peak of the spectral energy distribution shifting from 100 keV down to a few keV. However the thermal disk and the hard X-ray components had a similar intensity, indicating that the source was in an intermediate state throughout our observations and evolving toward the soft state. In the second part of our observations, the ASM/RXTE and SPI/INTEGRAL light curve showed a strong flaring activity. Two flare events lasting about 1 day each have been detected with SPI and are probably due to instabilities in the accretion disk associated with the state transition. During these flares, the low (1.5-12 keV) and high (20-200 keV) energy fluxes monitored with ASM/RXTE and SPI/INTEGRAL, are correlated and the spectral shape (above 20 keV) remains unchanged while the luminosity increases by a factor greater than 2., Comment: 26 pages, 7 figures, accepted for publication in Astrophysical Journal

On March 2003, IBIS, the gamma-ray imager on board the INTEGRAL satellite, detected an outburst from a new source, IGR J17464-3213, that turned out to be a HEAO-1 transient, H1743-322. In this paper we report on the high energy behaviour of this BHC studied with the three main instruments onboard INTEGRAL. The data, collected with unprecedented sensitivity in the hard X-Ray range, show a quite hard Comptonised emission from 3 keV up to 150 keV during the rising part of the source outburst, with no thermal emission detectable. A few days later, a prominent soft disk multicolour component appears, with the hard tail luminosity almost unchanged: 10-9 erg*cm-2*s-1. Two months later, during a second monitoring campaign near the end of the outburst, the observed disk component was unchanged. Conversely, the Comptonised emission from the central-hot part of the disk reduced by a factor of 10. We present here its long term behaviour in different energy ranges and the combined JEM-X, SPI and IBIS wide band spectral evolution of this source., Comment: 12 pages, 4 figures, accepted for pubblication in APJ

We present preliminary results of an observation of Cygnus X-1 with INTEGRAL performed on June 7-11 2003. Both spectral and variability properties of the source indicate that Cygnus X-1 was in an intermediate state. As expected during state transitions, we find an anticorrelation between the 3-10 keV and the 15 GHz radio fluxes and a strong correlation between the 3-200 keV hardness and radio flux., Comment: 4 pages, 8 figures, to appear in the proceedings of the 5th INTEGRAL workshop "The INTEGRAL Universe", (Munich, February 2004), ESA Special Publication SP-552

We present the analysis of the first observations of the Cygnus region by the SPI spectrometer onboard the Integral Gamma Ray Observatory, encompassing ${\sim}$ 600 ks of data. Three sources namely Cyg X-1, Cyg X-3 and EXO 2030+375 were clearly detected. Our data illustrate the temporal variability of Cyg X-1 in the energy range from 20 keV to 300 keV. The spectral analysis shows a remarkable stability of the Cyg X-1 spectra when averaged over one day timescale. The other goal of these observations is SPI inflight calibration and performance verification. The latest objective has been achieved as demonstrated by the results presented in this paper., Comment: 6 pages, 10 figures, accepted for publication in A&A (special INTEGRAL volume)

We present the results of the GRANAT/SIGMA hard X-/soft gamma-ray long-term monitoring of the Galactic Center (GC) region concerning the source GRO J1744-28, discovered on 1995 Dec. 2 by CGRO/BATSE. SIGMA observed the region containing the source in 14 opportunities between 1990 and 1997. In two of these observing sessions, corresponding to March 1996 and March 1997, GRO J1744-28 was detected with a confidence level greater than 5(sigma) in the 35-75 keV energy band without detection in the 75-150 keV energy band. For the other sessions, upper limits of the flux are indicated. The particular imaging capabilities of the SIGMA telescope allow us to identify, specifically, the source position in the very crowded GC region, giving us a mean flux of (73.1 +/- 5.5)E-11 and (44.7 +/- 6.4)E-11 ergs cm^-2 s^-1 in the 35-75 keV energy band, for the March 1996 and March 1997 observing sessions, respectively. Combining the March 1997 SIGMA and BATSE observations, we found evidence pointing to the type-II nature of the source bursts for this period. For the same observing campaigns, spectra were obtained in the 35 to 150 keV energy band. The best fit corresponds to an optically thin thermal Bremsstrahlung with F(50 keV)=(3.6 +/- 0.6)E-4 phot cm^-2 s^-1 keV^-1 and kT(Bremss)=28 +/- 7 keV, for the first campaign, and F(50 keV)=(2.3 +/- 0.7)E-4 phot cm^-2 s^-1 keV^-1 and kT(Bremss)=18 (+12/-7) keV, for the second. This kind of soft spectrum is typical of binary sources containing a neutron star as the compact object, in contrast to the harder spectra typical of systems containing a black hole candidate, Comment: Accepted for publication in the Astrophysical Journal, 4 pages, 4 figures

We present photometric ISO 60 and 170um measurements, complemented by some IRAS data at 60um, of a sample of 84 nearby main-sequence stars of spectral class A, F, G and K in order to determine the incidence of dust disks around such main-sequence stars. Of the stars younger than 400 Myr one in two has a disk; for the older stars this is true for only one in ten. We conclude that most stars arrive on the main sequence surrounded by a disk; this disk then decays in about 400 Myr. Because (i) the dust particles disappear and must be replenished on a much shorter time scale and (ii) the collision of planetesimals is a good source of new dust, we suggest that the rapid decay of the disks is caused by the destruction and escape of planetesimals. We suggest that the dissipation of the disk is related to the heavy bombardment phase in our Solar System. Whether all stars arrive on the main sequence surrounded by a disk cannot be established: some very young stars do not have a disk. And not all stars destroy their disk in a similar way: some stars as old as the Sun still have significant disks., Comment: 16 pages, 9 figures, Astron & Astrophys. in press

Using a non-linear Monte-Carlo code we investigate the radiative response of an accretion disk corona system to static homogeneous flares. We model a flare by a rapid (comparable to the light crossing time) energy dissipation in the corona or the disk. If the flares originate from the disk, the coronal response to the soft photon shots produces a strongly non-linear Comptonised radiation output, with complex correlation/anti-correlations between energy bands. This behavior strongly differs from those found with usual linear calculations. Thus any model for the rapid aperiodic variability of X-ray binaries invoking a varying soft photon input as a source for the hard X-ray variability has to take into account the coronal temperature response. On the other hand, if the flare is due to a violent heating of the corona, when the perturbation time scale is of the order of a few corona light crossing times, the shot spectrum evolves from hard to soft. This general trend is independent of the shot profile and geometry. We show that for short dissipation time, the time averaged spectra are generally harder than in steady state situation. In addition, annihilation line and high energy tails can be produced without need for non-thermal processes., Comment: 13 pages, 7 figures, to appear in Astronomy and Astrophysics

The inclusive 2H(3He,t) reaction has been studied at 2 GeV for energy transfers up to 500 MeV and scattering angles from 0.25 up to 4 degrees. Data are well reproduced by a model based on a coupled-channel approach for describing the NN and N Delta systems. The effect of final state interaction is important in the low energy part of the spectra. In the delta region, the cross-section is very sensitive to the effects of Delta-N interaction and Delta N - NN process. The latter has also a large influence well below the pion threshold. The calculation underestimates the experimental cross-section between the quasi-elastic and the delta peaks; this is possibly due to projectile excitation or purely mesonic exchange currents., Comment: 9 pages, 9 figures, accepted for publication in EPJA

The results of GRANAT/SIGMA hard X-ray observations of GRS 1758-258 in 1990-1998 are presented. The source lies at ~5\arcdeg from the Galactic Center and was within the SIGMA field of view during the GRANAT surveys of this region. The total exposure time of the Galactic Center was 11x10^6 s. The regular SIGMA observations revealed strong variability of the source: the 40-150 keV flux varied at least by a factor of 8 on a time scale of a year, between less than 13 mCrab and ~100-110 mCrab. The average flux was ~60 mCrab in 1990-1998. The source's spectrum is well fitted by a power law with a photon index \alpha ~1.86 in the energy range 40 to 150 keV and becomes steeper at energies above ~100 keV. The radio and hard X-ray properties of GRS 1758-258 are similar to those of another Galactic Center source, 1E1740.7-2942. GRS 1758-258 and 1E1740.7-2942 are the two brightest hard X-ray sources in the Galactic Center region. Both sources have radio jets, similar X-ray luminosities (~10^37 erg/s), and spectra, and exhibit variations in the hard X-ray flux on long times scales by a factor of ~10 or more . In contrast to most of the known black hole candidates, which are X-ray transients, GRS 1758-258 and 1E1740.7-2942 were detected by SIGMA during most of the observations in 1990-1998. Assuming that this behavior of the sources implies the suppression of accretion-disk instability in the region of partial hydrogen ionization through X-ray heating, we impose constraints on the mass of the optical companion and on the orbital period of the binary system., Comment: 18 pages with 5 figures. Astronomy Letters, 1999, 25 (in press)

We present a GRANAT/SIGMA observation of the soft gamma-ray afterglow immediately after GRB 920723. The main burst is very bright. After ~6 s, the burst light curve makes a smooth transition into an afterglow where flux decays as t^{-0.7}. The power-law decay lasts for at least 1000 s; beyond this time, the afterglow emission is lost in the background fluctuations. At least ~20% of main burst energy is emitted in the afterglow. At approximately ~6 s after the trigger, we also observe an abrupt change in the burst spectrum. At t<6 s, the ratio of 8-20 and 75-200 keV fluxes corresponds to the power law spectral index \alpha=0.0-0.3. At t=6 s, the value of \alpha increases to \alpha= ~1 and stays at this level afterwards. The observed afterglow characteristics are discussed in connection with the relativistic fireball model of gamma-ray bursts., Comment: 5 pages, 4 figures, submitted to Astronomy and Astrophysics Letters

The Center of the Milky Way emits radiation through all the electromagnetic spectrum due to the presence of several astrophysical phenomena. Various scientifical questions remain unsolved in the picture that emerge from observations, the main one being the presence and activity of a supermassive black hole at the Galactic Center. Also in the X-ray band a strong diffuse emission is detected up to 22 keV, it has been suggested that its origin is linked to past high energy activity of the Galactic Center. The French SIGMA soft gamma ray telescope on board the Russian Granat satellite observed the Galacti Center (GC) for abour 9 X 10^6 seconds from 1990 to the end of 1997. Its unique imaging capabilities coupled with the unprecedented exposure already allowed us to set preliminary constraints on the persistent high energy emission from Sgr A*. Here we present a new analysis of the complete set of observations of this region taking into account the possible presence of diffuse emission in the low energy channels. This allows us both to test current advection models of high energy emission from Sgr A* and to investigate on past high energy activity., Comment: 4 pages LateX, 1 Postscript Figure, To appear in the Proceedings of the 3rd INTEGRAL workshop, Taormina, Italy, 1998

We developed a non-linear Monte Carlo code based on the LP method proposed by Stern et al (1995). We use it to simulate an extended non-thermal X/gamma ray source coupled with a cold accretion disk. The source radiates by inverse Compton process. We show that very low optical depths are required for the 2nd Compton order to be negligible. Such optical depths can be reached only if the source is very close to the disk (corona-like geometries). And even in this configuration, 2nd Compton order is negligible only for the hardest observed spectral slopes. We also account for Compton reflection on the disk. This kind of coupling leads to a strongly angle dependent spectrum with a reflection component much stronger than in standard isotropic models, leading to unobserved reflection dominated spectra at low inclination., Comment: 5 pages, 6 figures, to be published in the proceedings of the 3rd INTEGRAL WORKSHOP