论文标题
向前偏双随机系统和路径依赖性随机PDES的经典解决方案
Forward-backward doubly stochastic systems and classical solutions of path-dependent stochastic PDEs
论文作者
论文摘要
在本文中，研究了一类非马克维亚前进的双向随机系统。通过使用功能性ITô（或依赖路径依赖性的）演算的技术，建立了系统与相关路径依赖性的准线性偏微分方程（简称SPDE）之间的关系，并建立了众所周知的非线性FEYNMAN-FEYNMAN-KAC peng spends pardoux和penghard spenderavers speveraper and pardwardd douebly doubly douebly douenial seconeratial systerations systemal systeart和系统。理论相关。 Fields 98（1994），第209--227页]是针对非马克维亚局势的。此外，我们获得了对向前偏双随机系统的溶液的可不同性，以及对路径依赖性SPDE的解决方案的某些特性。
In this paper, a class of non-Markovian forward-backward doubly stochastic systems is studied. By using the technique of functional Itô (or path-dependent) calculus, the relationship between the systems and related path-dependent quasi-linear stochastic partial differential equations (SPDEs in short) is established, and the well-known nonlinear stochastic Feynman-Kac formula of Pardoux and Peng [Backward doubly stochastic differential equations and systems of quasilinear SPDEs, Probab. Theory Relat. Fields 98 (1994), pp. 209--227] is developed to the non-Markovian situation. Moreover, we obtain the differentiability of the solution to the forward-backward doubly stochastic systems and some properties of solutions to the path-dependent SPDEs.
