BSDEs generated by fractional space-time noise and related SPDEs

Yaozhong Hu, Juan Li and Chao Mi

Applied Mathematics and Computation, 2023, vol. 450, issue C

Abstract: This paper is concerned with the backward stochastic differential equations whose generator is a weighted fractional Brownian field: Yt=ξ+∫tTYsW(ds,Bs)−∫tTZsdBs, 0≤t≤T, where W is a (d+1)-parameter weighted fractional Brownian field of Hurst parameter H=(H0,H1,⋯,Hd), which provide probabilistic interpretations (Feynman-Kac formulas) for certain linear stochastic partial differential equations with colored space-time noise. Conditions on the Hurst parameter H and on the decay rate of the weight are given to ensure the existence and uniqueness of the solution pair. Moreover, the explicit expression for both components Y and Z of the solution pair is given.

Keywords: Backward stochastic differential equations; Stochastic partial differential equations; Feynman-Kac formulas; Fractional space-time noise; Explicit solution; Malliavin calculus (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:450:y:2023:i:c:s0096300323001480

DOI: 10.1016/j.amc.2023.127979

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