Asymptotic Bismut formulae for stochastic functional differential equations with infinite delay

Wang, Ya; Wu, Fuke; Yin, George

doi:10.1090/proc/15966

Asymptotic Bismut formulae for stochastic functional differential equations with infinite delay
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by Ya Wang, Fuke Wu and George Yin PDF

Proc. Amer. Math. Soc. 150 (2022), 4037-4051 Request permission

Abstract:

Using Malliavin calculus, this paper establishes asymptotic Bismut formulae for stochastic functional differential equations with infinite delay. Both nondegenerate and degenerate diffusion coefficients are treated. In addition, combined with the corresponding exponential ergodicity, stabilization bounds for $\nabla P_{t}f$ as $t\rightarrow \infty$ are derived.

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