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We derive normal approximation bounds in the Wasserstein distance for sums of generalized U-statistics, based on a general distance bound for functionals of independent random variables of arbitrary distributions. Those bounds are applied to normal approximation for the combined weights of subgraphs in the Erdős–Rényi random graph, extending the graph counting results of Barbour et al. (A central limit theorem for decomposable random variables with applications to random graphs, J. Combin. Theory Ser. B 47(2) (1989), pp. 125–145) to the setting of weighted graphs. Our approach relies on a general stochastic analytic framework for functionals of independent random sequences. [ABSTRACT FROM AUTHOR]

We extend the construction of equilibria for linear-quadratic and mean-variance portfolio problems available in the literature to a large class of mean-field time-inconsistent stochastic control problems in continuous time. Our approach relies on a time discretization of the control problem via n-person games, which are characterized via the maximum principle using backward stochastic differential equations. The existence of equilibria is proved by applying weak convergence arguments to the solutions of n-person games. A numerical implementation is provided by approximating n-person games using finite Markov chains. [ABSTRACT FROM AUTHOR]

We derive a characterization of equilibrium controls in continuous-time, time-inconsistent control (TIC) problems using the Malliavin calculus. For this, the classical duality analysis of adjoint BSDEs is replaced with the Malliavin integration by parts. This results into a necessary and sufficient maximum principle which is applied to a linear-quadratic TIC problem, recovering previous results obtained by duality analysis in the mean-variance case, and extending them to the linear-quadratic setting. We also show that our results apply beyond the linear-quadratic case by treating the generalized Merton problem. [ABSTRACT FROM AUTHOR]

We construct unbiased estimators for the distribution of the number of points inside random stopping sets based on a Poisson point process. Our approach is based on moment identities for stopping sets, showing that the random count of points inside the complement S̅ of a stopping set S has a Poisson distribution conditionally to S. The proofs do not require the use of set-indexed martingales, and our estimators have a lower variance when compared to standard sampling. Numerical simulations are presented for examples such as the convex hull and the Voronoi flower of a Poisson point process, and their complements. [ABSTRACT FROM AUTHOR]

We construct Cournot games with limited demand, resulting into capped sales volumes according to the respective production shares of the players. We show that such games admit three distinct equilibrium regimes, including an intermediate regime that allows for a range of possible equilibria. When information on demand is modeled by a delayed diffusion process, we also show that this intermediate regime collapses to a single equilibrium while the other regimes approximate the deterministic setting as the delay tends to zero. Moreover, as the delay approaches zero, the unique equilibrium achieved in the stochastic case provides a way to select a natural equilibrium within the range observed in the no lag setting. Numerical illustrations are presented when demand is modeled by an Ornstein–Uhlenbeck process and price is an affine function of output. [ABSTRACT FROM AUTHOR]

In this paper, we consider fog radio access networks (F-RANs) consisting of cache-enabled device-to-device (D2D) transmitters and fog access points (F-APs), which deliver data by exploiting cached contents or leveraging cloud processing. We consider three types of modes at a typical user, namely, D2D, F-AP, and cooperative modes. In the D2D and the F-AP modes, when the user requests content, the user receives the content from a D2D transmitter and an F-AP caching the content, respectively. In the cooperative mode, F-APs located near the user send data aided by a centralized cloud processing unit. We also examine a mode selection algorithm in which the user adaptively selects one of the three modes. In practical scenarios, to mitigate interference, the transmitters may not be placed close to each other, and thus, there may exist a form of repulsion among the transmitters’ locations. In this context, we model the spatial distributions of the D2D transmitters and the F-APs as $\beta $ -Ginibre point processes, which reflect the repulsive behavior and contain the Poisson point process as a special case. Then, we provide analytical expressions for the coverage probabilities in the F-RANs. Our results are corroborated by Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

The fifth-generation (5G) wireless networks are expected to provision value-added services with ubiquitous coverage, which makes data security unprecedentedly critical. In this context, physical layer security has emerged as a promising solution to safeguard data transmission by exploiting characteristics of the wireless medium. Despite the recent technological advance in physical layer security and wireless transmission, secrecy outages (i.e., data breaches) and service outages (i.e., connection failures) will inevitably happen and incur financial losses. This economical consequence is a fact that is mostly overlooked by the existing literature. To provide financial protection against secrecy outage and service outage, we introduce a cyber-insurance framework for wireless users in cellular networks, where each user pays a premium to an insurer for a future financial compensation if an outage occurs to him/her. In particular, we derive the network risks of the cellular users in terms of secrecy outage probability and service outage probability as well as the financial risk of the cyber insurer in terms of the ruin probability that indicates the chance that the insurer experiences a deficit in affording the losses of outage users. Through numerical evaluation, we demonstrate the impact of network performance on the financial risk of the insurer. The numerical results also show that the ruin probability of the insurer can be effectively reduced by equipping a larger number of antennas at the base stations or increasing network frequency reuse. [ABSTRACT FROM AUTHOR]

We extend stochastic newsvendor games with information lag by including dynamic retail prices, and we characterize their equilibria. We show that the equilibrium wholesale price is a nonincreasing function of the demand, while the retailer's output increases with demand until we recover the usual equilibrium. In particular, it is then optimal for retailer and wholesaler to have demand at least equal to some threshold level, beyond which the retailer's output tends to an upper bound which is absent in fixed retail price models. When demand is given by a delayed Ornstein-Uhlenbeck process and price is an affine function of output, we numerically compute the equilibrium output and we show that the lagged case can be seen as a smoothing of the no lag case. [ABSTRACT FROM AUTHOR]

We propose a recursive algorithm for the numerical computation of the optimal value function $\inf _{t\le \tau \le T} \mathbb {E} \left [\sup _{0\le s\le T } Y_{s} / Y_{\tau } \left | {\mathcal F}_{t}\right .\right ] $ over the stopping times τ with respect to the filtration of a geometric Brownian motion Y with Markovian regime switching. This method allows us to determine the boundary functions of the optimal stopping set when no associated Volterra integral equation is available. It applies in particular when regime-switching drifts have mixed signs, in which case the boundary functions may not be monotone. [ABSTRACT FROM AUTHOR]

We derive Mellin integral representations in terms of Macdonald functions for the squared absolute value s ↦ | Γ ⁢ ( a + i ⁢ s ) | 2 {s\mapsto|\Gamma(a+is)|^{2}} of the gamma function and its Fourier transform when a < 0 {a<0} is non-integer, generalizing known results in the case a > 0 {a>0}.This representation is based on a renormalization argument using modified Bessel functions of the second kind, and it applies to the representation of the solutions of a Fokker–Planck equation. [ABSTRACT FROM AUTHOR]

We derive normal approximation bounds by the Stein method for stochastic integrals with respect to a Poisson random measure over ℝd, d ≥ 2. This approach relies on third cumulant Edgeworth-type expansions based on derivation operators defined by the Malliavin calculus for Poisson random measures. The use of third cumulants can exhibit faster convergence rates than the standard Berry- Esseen rate for some sequences of Poisson stochastic integrals. [ABSTRACT FROM AUTHOR]

The Poisson point process (PPP) has been widely employed to model wireless networks and analyze their performance. The PPP has the property that nodes are conditionally independent from each other. As such, it may not be a suitable model for many networks, where there exists repulsion among the nodes. In order to address this limitation, we adopt a Poisson hardcore process (PHCP), in which no two nodes can be closer than a repulsion radius from one another. We consider two-tier heterogeneous networks, where the spatial distributions of transmitters in the first-tier and the second-tier networks follow a PHCP and a PPP, respectively. To alleviate inter-tier interference, we consider a guard zone for the first-tier network and presume that the second-tier transmitters located in the zone are deactivated. Under this setup, the activated second-tier transmitters form a Poisson hard-core hole process. We first derive exact computable expressions of the coverage probability and introduce a method to efficiently evaluate the expressions. Then, we provide approximations of the coverage probability, which have lower computational complexities. In addition, as a special case, we investigate the coverage probability of single-tier networks by modeling the locations of transmitters as a PHCP. [ABSTRACT FROM PUBLISHER]

Wireless radio frequency energy harvesting has been adopted in wireless networks as a method to supply energy to wireless nodes. In this paper, we analyze a wireless energy harvesting network based on a Boolean-Poisson model. This model assumes that energy sources are distributed according to a Poisson point process and have disc-shaped coverage regions with random radii. We introduce a distribution for the coverage radii, which takes aggregated harvested power into account. The union of the coverage regions of the energy sources forms the energy harvesting zone. We derive the transmission success probability of single-hop networks characterized by the probability that two sensor nodes are located in the energy harvesting zone. Then, we analyze the performance of multi-hop networks in the cases, where the locations of the sensor nodes are either fixed or randomly distributed. Moreover, we consider a star-shaped topology, which reflects the scenario wherein some sensor nodes simultaneously transmit data to a data collector. In this setting, we derive an approximation of the average throughput at the data collector. Numerical results validate the accuracy of our analysis in the single-hop and multi-hop networks and confirm the tightness of our approximation in the case of the star-shaped topology. [ABSTRACT FROM PUBLISHER]

We establish an integration by parts formula for the random functionals of a continuous-time Markov chain, based on partial differentiation with respect to jump times. In comparison with existing methods, our approach does not rely on the Girsanov theorem and it imposes less restrictions on the choice of directions of differentiation, while assuming additional continuity conditions on the considered functionals. As an application we compute sensitivities (Greeks) using stochastic weights in an asset price model with Markovian regime switching. [ABSTRACT FROM PUBLISHER]