Existence of Invariant Measures for Reflected Stochastic Partial Differential Equations

Jasdeep Kalsi ()
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Jasdeep Kalsi: University of Oxford

Journal of Theoretical Probability, 2020, vol. 33, issue 3, 1755-1767

Abstract: 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.

Keywords: SPDE; Reflected SPDE; Invariant measure; 60H15 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10959-019-00906-z

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