The first exit time of the autoregressive process beyond a level and an application to the disorder problem. (Russian) Zbl 0702.60048

Novikov, A. A.

Teor. Veroyatn. Primen. 35, No. 2, 282-292 (1990).

The exit time \(\tau_ A\) of level A of an autoregressive first order stochastic process Y is investigated both for discrete and continuous time. A relation between E \(\tau\) \({}_ A\) and the expectation of an integral expression which includes \(Y_{\tau_ A}\) is established. Applications to the disorder problem are given.

Reviewer: F.Liese

MSC:

60G40

Stopping times; optimal stopping problems; gambling theory

Keywords:

autoregressive process; exit time; disorder problem