On a class of perturbed generators of stable processes. (English. Ukrainian original) Zbl 0943.60067

Löbus, J.-U.; Portenko, M. I.

Theory Probab. Math. Stat. 52, 109-118 (1996); translation from Teor. Jmovirn. Mat. Stat. 52, 102-111 (1995).

This article is the result of the authors’ attempts to construct a stable analog of the well-known skew Brownian motion. The attempt is unsuccessful, although the authors construct skew Brownian motion and obtain a semigroup of operators. But, unfortunately, this semigroup does not respect to any Markov process. However, the authors assert in the final remarks that there is a way for constructing a stable analog of the skew Brownian motion. But this right way will be passed only in another publication in detail.

Reviewer: A.V.Swishchuk (Kyïv)

MSC:

60J35	Transition functions, generators and resolvents
47D03	Groups and semigroups of linear operators
35S10	Initial value problems for PDEs with pseudodifferential operators
47D07	Markov semigroups and applications to diffusion processes
60J65	Brownian motion
60J60	Diffusion processes

Keywords:

generator; stable process; semigroups; pseudodifferential operator; diffusion process