One-dimensional continuous drift processes. (Russian) Zbl 0635.60085

Zakusilo, O. K.

Teor. Veroyatn. Mat. Stat., Kiev 37, 46-56 (1987).

Let \(X=(x(t),{\mathcal F}_ t,P_ x)\) be a one-dimensional continuous strong Markov process where (\({\mathcal F}_ t,t\geq 0)\) is the family of \(\sigma\)-fields generated by x(\(\cdot)\). Assume that there exists a stopping time \(\tau\) with the properties: a) \(P_ x(\tau >0)=1\), \(x\in R\); b) \(F_{\tau -}=\sigma (\tau)(mod P_ x)\), and c) \(\tau\) is a terminal time. We completely describe the structure of X.

Reviewer: O.K.Zakusilo

MSC:

60J25

Continuous-time Markov processes on general state spaces

Keywords:

strong Markov process; stopping time; terminal time