Measure-Valued Diffusions and Continual Systems of Interacting Particles in a Random Medium

  • A. Yu. Pilipenko Ин-т математики НАН Украины, Киев

Abstract

We consider continual systems of stochastic equations describing the motion of a family of interacting particles whose mass can vary in time in a random medium. It is assumed that the motion of every particle depends not only on its location at given time but also on the distribution of the total mass of particles. We prove a theorem on unique existence, continuous dependence on the distribution of the initial mass, and the Markov property. Moreover, under certain technical conditions, one can obtain the measure-valued diffusions introduced by Skorokhod as the distributions of the mass of such systems of particles.
Published
25.09.2005
How to Cite
PilipenkoA. Y. “Measure-Valued Diffusions and Continual Systems of Interacting Particles in a Random Medium”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, no. 9, Sept. 2005, pp. 1289–1301, https://umj.imath.kiev.ua/index.php/umj/article/view/3685.
Section
Research articles