One version of the Clark representation theorem for Arratia flow
The article contains description of the functionals from the family of coalescing Brownian particles. New type of the stochastic integral is introduced and used.
math.PR↗
arXiv subjects
Andrey A Dorogovtsev
Publications and source records attributed to Andrey A Dorogovtsev.
Smoothing problem in anticipating scenario
This article is devoted to the stochastic anticipating equations with the extended stochastic integral with respect to the Gaussian processes of a special type and its application to the smoothing problem in the case when noise is represented by the two jointly Gaussian Wiener processes, which can have not a semimartingale property with respect to the joint filtration.
math.PR↗
One Brownian Stochastic Flow
The weak limits of the measure-valued processes organized as a mass carried by the interacting Brownian particles are described. As a limiting flow the Arrattia flow is obtained.
math.PR↗
Stochastic anticipating boundary value problems
This article is devoted to the stochastic anticipating equations with the extended stochastic integral with respect to the Gaussian processes of a special type. In the particular cases the solutions of such an equations are the well-known Wiener functionals after the second quantization. As an application the stochastic Kolmogorov equation for the conditional distributions of the diffusion process is obtained. Also we will consider the conditional variant of the Feynman--Kac formula. The two last sections of the article are devoted to the smoothing problem in the case when noise is represented by the two jointly Gaussian Wiener processes, which can have not a semimartingale property with respect to the joint filtration.
math.PR↗