Bismut formula for a stochastic heat equation with fractional noise

Litan Yan and Xiuwei Yin

Statistics & Probability Letters, 2018, vol. 137, issue C, 165-172

Abstract: In this note, we establish the Bismut formula for stochastic heat equation ∂∂tu(t,x)=Δu(t,x)+ẆH(t,x),t≥0,x∈[0,1],∂∂xu(t,x)|x=0=∂∂xu(t,x)|x=1=0,t≥0,u(0,x)=f(x),x∈[0,1],where f(x)∈H≔L2([0,1]) and WH is the fractional noise with Hurst index H∈(12,1). As an application, we also introduce the Harnack inequality.

Keywords: Stochastic heat equation; Fractional noise; Bismut formula; Harnack inequality (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spl.2018.01.018

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