On Multidimensional Generalized Diffusion Processes

  • H. M. Shevchenko

Abstract

We construct a multidimensional generalized diffusion process with the drift coefficient that is the (generalized) derivative of a vector-valued measure satisfying an analog of the Hölder condition with respect to volume. We prove the existence and continuity of the density of transition probability of this process and obtain standard estimates for this density. We also prove that the trajectories of the process are solutions of a stochastic differential equation.
Published
25.09.2003
How to Cite
ShevchenkoH. M. “On Multidimensional Generalized Diffusion Processes”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 55, no. 9, Sept. 2003, pp. 1291-6, https://umj.imath.kiev.ua/index.php/umj/article/view/4003.
Section
Research articles