Reflecting Brownian motion in $d$-ball

Authors: Pavel Ievlev
Published in: Zap. Nauchn. Sem. POMI (2019)
Date:

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

Details

Untitled

Overview

Detailed description of the publication, methodology, results, and impact.

Key Contributions

  • Contribution 1
  • Contribution 2
  • Contribution 3

Methodology

Brief description of the approach used.

Results

Summary of key findings.

Impact

Discussion of the paper’s significance and citations.

Citation

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}
}