Geodesic
Reflecting Lévy processes and associated families of linear operators
Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 3, pp. 417-441 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper is concerned with special one-dimensional Markov processes, which are Lévy processes defined on a finite interval and reflected from the boundary points of the interval. It is shown that in this setting, 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. In the case when the original process is a Wiener process, we show that these operators can be expressed in terms of the local time of the process on the boundary of the interval.
Keywords: random process, initial boundary value problem, limit theorem, local time. 
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I. A. Ibragimov; N. V. Smorodina; M. M. Faddeev. Reflecting Lévy processes and associated families of linear operators. Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 3, pp. 417-441. http://geodesic.mathdoc.fr/item/TVP_2019_64_3_a0/

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