论文标题
分数时空噪声和相关SPDE产生的BSDE
BSDEs generated by fractional space-time noise and related SPDEs
论文作者
论文摘要
This paper is concerned with the backward stochastic differential equations whose generator is a weighted fractional Brownian field: $Y_t=ξ+\int_t^T Y_s W (ds,B_s) -\int_t^T Z_sdB_s$, $0\le t\le T$, where $W$ is a $(d+1)$-parameter weighted fractional Brownian field of Hurst parameter $ h =（h_0，h_1，\ cdots，h_d）$，它为具有彩色时空噪声的某些线性随机偏微分方程提供了概率解释（Feynman-kac公式）。赫斯特参数$ h $和重量的衰减率的条件是确保解决方案对的存在和独特性的。此外，给出了解决方案对的两个组件$ y $和$ z $的明确表达式。
This paper is concerned with the backward stochastic differential equations whose generator is a weighted fractional Brownian field: $Y_t=ξ+\int_t^T Y_s W (ds,B_s) -\int_t^T Z_sdB_s$, $0\le t\le T$, where $W$ is a $(d+1)$-parameter weighted fractional Brownian field of Hurst parameter $H=(H_0, H_1, \cdots, H_d)$, 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 are given.
