Asymptotic relation for the density of a multidimensional random evolution with rare poisson switchings

  • A. D. Kolesnik

Abstract

In the Euclidean space $\mathbb{R}^m,\quad m \geq 2,$ the symmetric random evolution $\textbf{X}(t) = (X_1(t),...,X_m(t))$ controlled by a homogeneous Poisson process with parameter $\lambda > 0$ is considered.
An asymptotic formula for the transition density $p(\textbf{x},t),\quad t > 0,$ of the process $\textbf{X}(t)$ for $\lambda \rightarrow 0$ is obtained. The behavior of $p(\textbf{x},t)$ near the boundary of the diffusion area in spaces of various dimensions is described.
Published
25.12.2008
How to Cite
Kolesnik, A. D. “Asymptotic Relation for the Density of a Multidimensional Random Evolution With Rare Poisson Switchings”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, no. 12, Dec. 2008, pp. 1631 -, https://umj.imath.kiev.ua/index.php/umj/article/view/3277.
Section
Research articles