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

• Date: 2008
• Main Authors: Kolesnik, A. D., Колесник, А. Д.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2008
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3277
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 &gt...