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Stationary solutions of retarded Ornstein-Uhlenbeck processes in Hilbert spaces

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  • Liu, Kai

Abstract

In this note, we shall study a class of retarded Langevin equations in infinite-dimensional spaces. An informative description of stationary solutions is given by means of Green operators, Lyapunov equations, the second moment bounds and retarded point spectrum. The covariance operator of the stationary solution is described as a solution of some retarded operator equation.

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  • Liu, Kai, 2008. "Stationary solutions of retarded Ornstein-Uhlenbeck processes in Hilbert spaces," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1775-1783, September.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:13:p:1775-1783
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    Cited by:

    1. Zhi Li & Litan Yan, 2019. "Ergodicity and Stationary Solution for Stochastic Neutral Retarded Partial Differential Equations Driven by Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1399-1419, September.
    2. Luo, Jiaowan & Lan, Guolie, 2009. "Stochastically bounded solutions and stationary solutions of stochastic differential equations in Hilbert spaces," Statistics & Probability Letters, Elsevier, vol. 79(21), pages 2260-2265, November.
    3. Kai Liu, 2012. "On Regularity Property of Retarded Ornstein–Uhlenbeck Processes in Hilbert Spaces," Journal of Theoretical Probability, Springer, vol. 25(2), pages 565-593, June.

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