A Class of $\mathbb{F}$-Doubly Stochastic Markov Chains

Abstract

We define a new class of processes, very useful in applications, $\mathbb{F}$-doubly stochastic Markov chains which contains among others Markov chains. This class is fully characterized by s ome martingale properties, and one of them is new even in the case of Markov chains. Moreover a predictable representation theorem holds and doubly stochastic property is preserved under natural change of measure.