abstract
- © 2022 Walter de Gruyter GmbH, Berlin/Boston 2022.In this paper, we consider a new telegraph process of Ornstein-Uhlenbeck type. The process is obtained by generalizing the telegraph process in a similar manner to how the Ornstein-Uhlenbeck process was obtained from the Wiener process, namely by adding a drift coefficient proportional to a displacement from the origin. This process was first introduced by Ratanov in [N. Ratanov, Ornstein-Uhlenbeck process of bounded variation, Methodol. Comput. Appl. Probab. 23 2021, 925-946]. We obtain the infinitesimal operator of this process and we present formulas for finding its stationary probability density. We consider both the symmetric and asymmetric cases.