Stochastic differential equations for infinite particle systems of jump type with long range interactions

Abstract

Infinite dimensional stochastic differential equations (ISDEs) describing systems with an infinte number of particles are considered. Each paticles undergo Lévy process, and interaction between particles is given by long range interaction poteintial, which is not necessary of Ruelle's class but also logarthmic. We discuss the existence and uniqueness of solutions of ISDEs.