Geodesic
Reflecting L\'evy processes and associated families of linear operators.~II
Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 1, pp. 23-36

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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 $L_2$ 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.
Keywords: random processes, initial-boundary problems, limit theorems, local time. 
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     title = {Reflecting {L\'evy} processes and associated families of linear {operators.~II}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2022_67_1_a1/}
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I. A. Ibragimov; N. V. Smorodina; M. M. Faddeev. Reflecting L\'evy processes and associated families of linear operators.~II. Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 1, pp. 23-36. http://geodesic.mathdoc.fr/item/TVP_2022_67_1_a1/