Approximation of stationary solutions of Gaussian driven stochastic differential equations

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:121

Article

Cohen, Serge³  Panloup, Fabien^1,2 

[1] Univ Toulouse, Lab Stat & Probabilites, F-31077 Toulouse 4, France

[2] INSA Toulouse, F-31077 Toulouse 4, France

[3] Univ Toulouse, Inst Math Toulouse, F-31062 Toulouse 9, France

关键词: Stochastic differential equation;    Gaussian process;    Stationary process;    Euler scheme;   

DOI  :  10.1016/j.spa.2011.08.001

来源: Elsevier

【 摘 要 】

We study sequences of empirical measures of Euler schemes associated to some non-Markovian SDEs: SDEs driven by Gaussian processes with stationary increments. We obtain the functional convergence of this sequence to a stationary solution to the SDE. Then, we end the paper by some specific properties of this stationary solution. We show that, in contrast to Markovian SDEs, its initial random value and the driving Gaussian process are always dependent. However, under an integral representation assumption, we also obtain that the past of the solution is independent of the future of the underlying innovation process of the Gaussian driving process. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

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