A generalized class of Lyons-Zheng processes

Abstract

Generalizing work by Lyons and Zheng, we study Dirichlet processes admitting a decomposition into the sum of a forward and a backward local martingale plus a bounded variation process. We develop a framework of stochastic calculus for these processes and deal with existence and uniqueness for stochastic differential equations driven by such processes. In particular, Bessel processes turn out to be an interesting example of Lyons-Zheng processes.