The first-passage area of Ornstein-Uhlenbeck process revisited

Abstract

For Ornstein-Uhlenbeck process starting from we highlight some results about the first-passage time of X(t) through zero and its first-passage area, that is the random area swept out by till its first-passage through zero. We study single and joint moments of the first-passage time and first-passage area, and their behaviors, as and moreover, we investigate the expected value of the time average of X(t) till the FPT, and the maximum displacement of