Reflecting Brownian motion in $d$-ball

Authors: Pavel Ievlev

Published in: Zap. Nauchn. Sem. POMI (2019)

Date: January 2019

Abstract

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 $d$-ball. The main advantage of our new approach is that it allows one to construct reflecting Lévy processes, whereas previous constructions are limited to diffusion processes. In our upcoming work we shall extend the results to the symmetric Levy processes in a smooth domain.

Keywords

Brownian motion with reflection, Markov semigroup

BibTeX

@article {MR4060234,
    AUTHOR = {Ievlev, P. N.},
    TITLE = {Reflecting {B}rownian motion in {$d$}-ball},
    JOURNAL = {Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov.              (POMI)},
    FJOURNAL = {Rossi\u iskaya Akademiya Nauk. Sankt-Peterburgskoe Otdelenie.              Matematicheski\u i\ Institut im. V. A. Steklova. Zapiski Nauchnykh Seminarov (POMI)},
    VOLUME = {486},
    YEAR = {2019},     
    PAGES = {158--177},
    ISSN = {0373-2703},
    MRCLASS = {60J65 (60G51)},
    MRNUMBER = {4060234}
}