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Random Operators and Stochastic Equations

Editor-in-Chief: Girko, Vyacheslav

Managing Editor: Molchanov, S.

Editorial Board: Accardi, L. / Albeverio, Sergio / Carmona, R. / Casati, G. / Christopeit, N. / Domanski, C. / Drygas, Hilmar / Gupta, A.K. / Ibragimov, I. / Kirsch, Werner / Klein, A. / Kondratyev, Yuri / Kurotschka, V. / Leonenko, N. / Loubaton, Philippe / Orsingher, E. / Pastur, L. / Rodrigues, Waldyr A. / Shiryaev, Albert / Turbin, A.F. / Veretennikov, Alexandre

CiteScore 2018: 0.26

SCImago Journal Rank (SJR) 2018: 0.142
Source Normalized Impact per Paper (SNIP) 2018: 0.375

Mathematical Citation Quotient (MCQ) 2018: 0.11

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Volume 18, Issue 1


Duality and semi-group property for backward parabolic Itô equations

Nikolai Dokuchaev
  • Department of Mathematics and Statistics, Curtin University of Technology, GPO Box U1987, Perth, Western Australia. E-mail:
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Published Online: 2010-03-17 | DOI: https://doi.org/10.1515/rose.2010.51


We study existence, uniqueness, semi-group property and a-priori estimates for solutions of backward parabolic Itô equations in domains with boundary. We study also duality between forward and backward equations. The semi-group for backward equations is established in the form of some anti-causality. The novelty is that the semi-group property involves the diffusion term that is a part of the solution.

Keywords.: Parabolic Itô equations; backward SPDEs; regularity; semi-group property; anti-causality

About the article

Received: 2009-07-06

Published Online: 2010-03-17

Published in Print: 2010-03-01

Citation Information: Random Operators and Stochastic Equations, Volume 18, Issue 1, Pages 51–72, ISSN (Online) 1569-397x, ISSN (Print) 0926-6364, DOI: https://doi.org/10.1515/rose.2010.51.

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