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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 2017: 0.32

SCImago Journal Rank (SJR) 2017: 0.177
Source Normalized Impact per Paper (SNIP) 2017: 0.592

Mathematical Citation Quotient (MCQ) 2017: 0.12

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Volume 21, Issue 3


An ergodic-type theorem for generalized Ornstein–Uhlenbeck processes

Andriy Yurachkivsky
Published Online: 2013-08-03 | DOI: https://doi.org/10.1515/rose-2013-0011


Let be an ℝd-valued càdlàg random process, and let F be an increasing from zero ℝ-valued random process whose values at all times are measurable w.r.t. some σ-algebra (the class of all such processes is denoted by ). Conditions guaranteing that for every bounded continuous function

are found. In the most general theorem they are formulated in terms of F and . Further we consider the case when satisfies an equation of the kind

where is an -measurable random variable, is a continuous process of class , A is a matrix-valued random process -measurable in , and S is an ℝd-valued semimartingale with conditionally on independent increments and initial value 0. In this case, sufficient conditions for () are stated in terms of F and the constituents of the equation. Besides, the characteristic function of an n-dimensional distribution of is found.

Keywords: Semimartingale; random measure; Ito formula; characteristic function

About the article

Received: 2011-05-09

Revised: 2012-12-19

Accepted: 2013-01-31

Published Online: 2013-08-03

Published in Print: 2013-09-01

Citation Information: Random Operators and Stochastic Equations, Volume 21, Issue 3, Pages 217–269, ISSN (Online) 1569-397X, ISSN (Print) 0926-6364, DOI: https://doi.org/10.1515/rose-2013-0011.

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