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Reflecting Lévy processes and associated families of linear operators. (English. Russian original) Zbl 1480.60213

Theory Probab. Appl. 64, No. 3, 335-354 (2019); translation from Teor. Veroyatn. Primen. 64, No. 3, 417-441 (2019).

MSC:

60J25 Continuous-time Markov processes on general state spaces
60G51 Processes with independent increments; Lévy processes
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
47D07 Markov semigroups and applications to diffusion processes
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References:

[1] A. V. Skorokhod, Stochastic equations for diffusion processes in a bounded region, Theory Probab. Appl., 6 (1961), pp. 264–274.
[2] A. Pilipenko, An Introduction to Stochastic Differential Equations with Reflection, Lectures in Pure Appl. Math. 1, Universitätsverlag, Potsdam, 2014.
[3] I. A. Ibragimov, N. V. Smorodina, and M. M. Faddeev, Initial boundary value problems in a bounded domain: Probabilistic representations of solutions and limit theorems. I, Theory Probab. Appl., 61 (2017), pp. 632–648. · Zbl 06823440
[4] I. A. Ibragimov, N. V. Smorodina, and M. M. Faddeev, Initial boundary value problems in a bounded domain: Probabilistic representations of solutions and limit theorems. II, Theory Probab. Appl., 62 (2018), pp. 356–372. · Zbl 1406.35090
[5] K. Sato and H. Tanaka, Local times on the boundary for multidimensional reflecting diffusion, Proc. Japan Acad., 38 (1962), pp. 699–702. · Zbl 0138.11302
[6] K. Itô and H. P. McKean, Jr., Diffusion Processes and Their Sample Paths, Grundlehren Math. Wiss. 125, Academic Press, New York, 1965.
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