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Reflecting Brownian Motion in the d-Ball

Following the works of I. A. Ibrahimov, N. V. Smorodina and M. M. Faddeev, we develop a new construction of the Brownian motion with reflection in the d-ball. The main advantage of our new approach is that it allows one to construct reflecting Levy processes, whereas previous constructions are limited to diffusion processes. In our upcoming work, we shall extend the results to symmetric Lévy processes in a smooth domain.

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Correspondence to P. N. Ievlev.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 486, 2019, pp. 158–177.

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Ievlev, P.N. Reflecting Brownian Motion in the d-Ball. J Math Sci 258, 845–858 (2021).

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