Applications of the graphs to the Generalized Ornstein-Uhlenbeck process

Abstract

We consider the generalized Ornstein- Uhlenbeck equation $\partial_t X=-m X_t+\eta$. In this paper We construct the L\'evy noise $\eta$. The generalized Ornstein- Uhlenbeck process $X_t$ will be represented by a special types of graphs called rooted trees with two types of leaves.