THE ANALYTICAL SOLUTION OF TWO PARAMETERS ORNSTEIN-UHLENBECK PROCESS

Pat Vatiwutipong; Nattakorn Phewchean

Pat Vatiwutipong
Nattakorn Phewchean

Keywords: Ornstein-Uhlenbeck process, stochastic differential equation, Wiener process, Gaussian and Markovian process

Abstract

The Ornstein-Uhlenbeck process is a well-known process which was wildly applied. This paper introduces the two parameters OrnsteinUhlenbeck process, which is a simple extension of this process, by allowing two processes to depend on each other. In our research, we derive the analytical solution of our new process. Also, we investigate its properties, and give the condition for mean-reversion property. Moreover, some numerical examples are given to illustrate our result.