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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

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Volume 7, Issue 4


On Multidimensional SDEs Without Drift and with A Time-Dependent Diffusion Matrix

H. J. Engelbert
  • Institut für Stochastik, Friedrich-Schiller-Universität, Ernst-Abbe Platz 1–4, D-07743 Jena, Germany. E-mail:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ V. P. Kurenok
  • Department of Mathematics and Mechanics, Belorussian State University, F. Skoriny Av. 4, 220050 Minsk, Belarus. E-mail:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2010-02-23 | DOI: https://doi.org/10.1515/GMJ.2000.643


We study multidimensional stochastic equations

where x o is an arbitrary initial state, W is a d-dimensional Wiener process and is a measurable diffusion coefficient. We give sufficient conditions for the existence of weak solutions. Our main result generalizes some results obtained by A. Rozkosz and L. Słomiński [Stochastics Stochasties Rep. 42: 199–208, 1993] and T. Senf [Stochastics Stochastics Rep. 43: 199–220, 1993] for the existence of weak solutions of one-dimensional stochastic equations and also some results by A. Rozkosz and L. Słomiński [Stochastic Process. Appl. 37: 187–197, 1991], [Stochastic Process. Appl. 68: 285–302, 1997] for multidimensional equations. Finally, we also discuss the homogeneous case.

Key Words and phrases:: Multidimensional stochastic differential equations; measurable coefficients; diffusion processes; martingales; Wiener process; weak convergence

About the article

Received: 2000-07-24

Published Online: 2010-02-23

Published in Print: 2000-12-01

Citation Information: Georgian Mathematical Journal, Volume 7, Issue 4, Pages 643–664, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/GMJ.2000.643.

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