Speaker: Zhihui Liu, Researcher, Department of Mathematics, Southern University of Science and Technology

Date: April 12, 2024

Time: 10:30-11:30

Location: B924, Zhixin Building, Shandong University

Sponsor: School of Mathematics, Shandong University

Abstract:

We establish the unique ergodicity of the Markov chain generated by thestochastic theta method (STM) with θ∈[½, 1] for monotone SODEs without growth restriction on the coefficients, driven by nondegenerate multiplicative noise. We also generalize the arguments to a class of monotone SPDEs driven by infinite-dimensional nondegenerate multiplicative trace-class noise. Applying these results to the stochastic Allen-Cahn equation indicates that its drift-implicit Euler scheme is uniquely ergodic for any interface thickness.

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