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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jebo.2004.07.015 Byline: Jaume Masoliver (a), Miquel Montero (a), Josep Perello (a), George H. Weiss (b) Keywords: Continuous time random walk; Volatility; Financial markets; Market microstructure Abstract: We adapt continuous time random walk (CTRW) formalism to describe asset price evolution and discuss some of the problems that can be treated using this approach. We basically focus on two aspects: (i) the derivation of the price distribution from high-frequency data, and (ii) the inverse problem, obtaining information on the market microstructure as reflected by high-frequency data knowing only the daily volatility. We apply the formalism to financial data to show that the CTRW offers alternative tools to deal with several complex issues of financial markets. Author Affiliation: (a) Departament de Fisica Fonamental, Universitat de Barcelona, Diagonal, 647, 08028-Barcelona, Spain (b) 1105 N. Belgrade Rd. Silver Spring, Md 20902, USA Article History: Received 26 September 2003; Accepted 21 July 2004

The rate constants for slow transitions between two states, which are characterized by different lifetimes of a fluorescent probe in the conformational interconversion of individual molecules in condensed phase, are measured by using single-molecule fluorescence spectroscopy. The sampling error for the estimates are derived based on the assumption that the data are gathered on M molecules, each monitored for a time T.

Statistical properties of the expected amount of time spent by a photon at different depths of a semi-infinite turbid medium are derived with formalism based on the continuous-time random walk. The formalism is applied to the study of both cw and time-gated experiments. Earlier analytical results relating to cw experiments are reproduced with a single approximation, rather than the more complicated approach used in earlier research based on the discrete-time random walk. The distribution of the occupancy of different depths in a time-gated experiment is found te have a convenient scaling form.

By applying a random-walk model for photon migration, we find an exact expression for fluorescent signals emitted from a homogeneous, optically turbid medium containing a single fluorescent mass. In contrast to diffusion-theory-based models, our analysis accounts for multiple photon passages through the fluorophore sites and allows for a variable degree of fluorescent absorptivity. We particularly discuss effects on the amplitudes and phase shifts of frequency-domain fluorescent signals.

Myocardial blood flow (rMBF) can be measured using dynamic positron emission tomography (PET) and bolus injection of [[H.sub.2].sup.15]O. Recent studies indicate that large errors in the estimates of flow [Mathematical Expression Omitted] can be produced by time shifts between the true arterial input function and the measured input function [A(t)]. We have investigated this phenomenon further using A(t) derived from patient data, and using simulated myocardial time activity curves [M(t)]. We found that with judicious choice of scan parameters and region of interest (ROI) placement, these errors can be greatly reduced. In particular, when A(t) is measured from the left ventricular (LV) cavity, the bias in [Mathematical Expression Omitted] is negligible over a wide range of circumstances. However, when A(t) is not measured from the LV cavity, the bias in flow can be large for short scans (< 2 min) or low flow values (f < 0.4 ml/g/min). We show that the bias is primarily due to the spill-over term in the model that is most commonly used to compute rMBF and suggest some correction methods. We conclude that it is possible to avoid errors in estimates of flow due to time delay. Index Terms - Blood flow, cardiac imaging, Kety model, positron emission tomography.