We obtain a class of higher-degree stochastic integration filters (SIF) for nonlinear filtering applications. SIF are based on stochastic spherical-radial integration rules that achieve asymptotically exact evaluations of Gaussian weighted multivariate integrals found in nonlinear Bayesian filtering. The superiority of the proposed scheme is demonstrated by comparing the performance of the prop...

The objective of this paper is to investigate natural transform Meijer’s G-Function in which Riemann–Liouville integrals are replaced by more general Prabhakar integrals. We analyze and discuss its properties terms Mittag-Leffler functions. Further, we show some applications these classical equations mathematical physics, like the heat free electron laser equations, difference-differential gove...

Donsker's invariance principle is shown to hold for random walks in rough path topology. As application, we obtain Donsker-type weak limit theorems for stochastic integrals and differential equations.

Let X = (Xt,Ft)t≥0 be a continuous local martingale with quadratic variation process 〈X〉 and X0 = 0. Define iterated stochastic integrals In(X) = (In(t, X),Ft) (n ≥ 0), inductively by

THIS BOOK is concerned with dynamical systems described by stochastic differential equations. The first part of the book deals with the analysis of such systems and the remainder of the book is on application to the filtering problem. The stochastic term driving the dynamical system is taken to be an arbitrary process with independent increments, so that the usual Wiener process model is consid...

A stochastic solution is constructed for a fractional generalization of the KPP (Kolmogorov, Petrovskii, Piskunov) equation. The solution uses a fractional generalization of the branching exponential process and propagation processes which are spectral integrals of Levy processes.

We show that, in general, inequalities between integrands with respect to Brownian motion do not lead to majorization in the convex order for the corresponding stochastic integrals. Particular examples and counter-examples are discussed.

Using the Malliavin calculus with respect to Gaussian processes and the multiple stochastic integrals we derive Itô’s and Tanaka’s formulas for the d-dimensional bifractional Brownian motion. 2000 AMS Classification Numbers: 60G12, 60G15, 60H05, 60H07.

We consider generalized adapted stochastic integrals with respect to independently scattered random measures with second moments, and use a decoupling technique, formulated as a “principle of conditioning”, to study their stable convergence towards mixtures of infinitely divisible distributions. The goal of this paper is to develop the theory. Our results apply, in particular, to Skorohod integ...