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Existence of Invariant Measures for Reflected Stochastic Partial Differential Equations

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  • Jasdeep Kalsi

    (University of Oxford)

Abstract

In this article, we close a gap in the literature by proving existence of invariant measures for reflected stochastic partial differential equations with only one reflecting barrier. This is done by arguing that the sequence $$(u(t,\cdot ))_{t \ge 0}$$ ( u ( t , · ) ) t ≥ 0 is tight in the space of probability measures on continuous functions and invoking the Krylov–Bogolyubov theorem. As we no longer have an a priori bound on our solution as in the two-barrier case, a key aspect of the proof is the derivation of a suitable $$L^p$$ L p bound which is uniform in time.

Suggested Citation

  • Jasdeep Kalsi, 2020. "Existence of Invariant Measures for Reflected Stochastic Partial Differential Equations," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1755-1767, September.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:3:d:10.1007_s10959-019-00906-z
    DOI: 10.1007/s10959-019-00906-z
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    References listed on IDEAS

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    1. Juan Yang & Tusheng Zhang, 2014. "Existence and Uniqueness of Invariant Measures for SPDEs with Two Reflecting Walls," Journal of Theoretical Probability, Springer, vol. 27(3), pages 863-877, September.
    2. Xu, Tiange & Zhang, Tusheng, 2009. "White noise driven SPDEs with reflection: Existence, uniqueness and large deviation principles," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3453-3470, October.
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