Martingales and first-passage times for Ornstein-Uhlenbeck processes with a jump component. (English. Russian original) Zbl 1056.60039

Novikov, A. A.

Theory Probab. Appl. 48, No. 2, 288-303 (2003); translation from Teor. Veroyatn. Primen. 48, No. 2, 340-358 (2003).

Using martingale technique, this paper shows that a distribution of the first-passage time over a level for the Ornstein-Uhlenbeck process with jumps is exponentially bounded. In the case of absence of positive jumps, the Laplace transform for this passage time is found. Further, the maximal inequalities are also given when the marginal distribution is stable.

Reviewer: Yuhu Feng (Shanghai)

MSC:

60G44	Martingales with continuous parameter
60H05	Stochastic integrals

Keywords:

exponential martingale; first-passage times; Ornstein-Uhlenbeck process, Laplace transform, moment Wald’s identity; maximal inequalities; stable distribution