由无穷个Brown单驱动的随机微分方程解的存在唯一性

Existence and Pathwise Uniqueness of Solutions to Stochastic Differential Equations Driven by Countably Many Brownian Sheets,

考虑如下一维双参数随机微分方程: ,其中{Wj,j=1,2,…}为一列无穷个相互独立的实值Brown单．作者定义关于无穷个Brown单的随机积分,并给出方程在非Lipschitz系数的条件下解的存在唯一性的一个结果．

Consider the one dimensional two parameter SDE： Xz=x＋∑^∞ j=1 ∫Rzσj（Xξ）dW^jξ,＋∫Rzb（Xξ）,where W^j is an infinite sequence of independent Brownian sheets,j=1,2,…The authors define stochastic integrals with respect to countably many Brownian sneers, and prove a theorem on the existence and uniqueness of solutions with non-Lipschitz coefficients.