Some Generalizations of Dynamic Stochastic Approximation Processes

Some Generalizations of Poisson Processes

In this paper we make an attempt to review count data models developed so far as generalizations of Poisson process. We consider Winkleman’s gamma count model and the Weibull count model of Mc Shane et al. The fractional generalization of Poisson process by Mainardi et al. is also considered. A Mittag-Leffler count model is developed and studied in detail. Simulation studies are also conducted.

Free-knot spline approximation of stochastic processes

We study optimal approximation of stochastic processes by polynomial splines with free knots. The number of free knots is either a priori fixed or may depend on the particular trajectory. For the s-fold integrated Wiener process as well as for scalar diffusion processes we determine the asymptotic behavior of the average Lp-distance to the splines spaces, as the (expected) number k of free knot...

Stochastic Analysis of Dynamic Processes

A Survey and Some Generalizations of Bessel Processes

Bessel processes play an important role in financial mathematics because of their strong relation to financial processes like geometric Brownian motion or CIR processes. We are interested in the first time Bessel processes and more generally, radial Ornstein–Uhlenbeck processes hit a given barrier. We give explicit expressions of the Laplace transforms of first hitting times by (squared) radial...

Using Learning for Approximation in Stochastic Processes

To monitor or control a stochastic dynamic system, we need to reason about its current state. Exact inference for this task requires that we maintain a complete joint probability distribution over the possible states, an impossible requirement for most processes. Stochastic simulation algorithms provide an alternative solution by approximating the distribution at time via a (relatively small) s...