Ergodic Properties of generalized Ornstein � Uhlenbeck Processes

Abstract

Let an -valued random process ? be the solution of an equation of the kind ?(t) = ?(0) +, where ?(0) is a random variable measurable w. r. t. some ?-algebra , S is a random process with-conditionally independent increments, ? is a continuous numeral random process of locally bounded variation, and A is a matrix-valued random process such that for any. Conditions guaranteing the existence of the limiting, as t ? ?, distribution of ?(t) are found. The characteristic function of this distribution is written explicitly. An ergodic theorem for generalized Ornstein Uhlenbeck processes is proved.