TY - JOUR

T1 - REFLECTING LÉVY PROCESSES AND ASSOCIATED FAMILIES OF LINEAR OPERATORS. II

AU - Ibragimov, I. A.

AU - Smorodina, N. V.

AU - Faddeev, M. M.

N1 - Publisher Copyright: © by SIAM.

PY - 2022

Y1 - 2022

N2 - We consider special one-dimensional Markov processes, namely, asymmetric jump Lévy processes, which have values in a given interval and reflect from the boundary points. We show that in this case, in addition to the standard semigroup of operators generated by the Markov process, there also appears the family of “boundary” random operators that send functions defined on the boundary of the interval to elements of the space L2 on the entire interval. This study is a continuation of our paper [Theory Probab. Appl., 64 (2019), 335–354], where a similar problem was solved for symmetric reflecting Lévy processes.

AB - We consider special one-dimensional Markov processes, namely, asymmetric jump Lévy processes, which have values in a given interval and reflect from the boundary points. We show that in this case, in addition to the standard semigroup of operators generated by the Markov process, there also appears the family of “boundary” random operators that send functions defined on the boundary of the interval to elements of the space L2 on the entire interval. This study is a continuation of our paper [Theory Probab. Appl., 64 (2019), 335–354], where a similar problem was solved for symmetric reflecting Lévy processes.

KW - initial-boundary problems

KW - limit theorems

KW - local time

KW - random processes

UR - http://www.scopus.com/inward/record.url?scp=85130994615&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/caa4c565-6620-3082-b041-c48f15c84c24/

U2 - 10.1137/s0040585x97t990721

DO - 10.1137/s0040585x97t990721

M3 - Article

AN - SCOPUS:85130994615

VL - 67

SP - 17

EP - 27

JO - Theory of Probability and its Applications

JF - Theory of Probability and its Applications

SN - 0040-585X

IS - 1

ER -