论文标题
随机功能微分方程的路径依赖性随机Gronwall不平等和强收敛率
A path-dependent stochastic Gronwall inequality and strong convergence rate for stochastic functional differential equations
论文作者
论文摘要
我们得出了一个随机的毛墙引理，在假定的仿生线性生长假设的上限的路径上具有顶部。这允许将应用程序的应用具有系数，这些系数取决于较早的时间点，例如随机延迟方程或随机微分方程的Euler型近似。我们将随机的毛墙引理与路径 - 苏普雷玛应用于随机的功能微分方程，并证明依赖路径 - 苏普雷玛的系数功能具有很强的收敛速率。
We derive a stochastic Gronwall lemma with suprema over the paths in the upper bound of the assumed affine-linear growth assumption. This allows applications to Itô processes with coefficients which depend on earlier time points such as stochastic delay equations or Euler-type approximations of stochastic differential equations. We apply our stochastic Gronwall lemma with path-suprema to stochastic functional differential equations and prove a strong convergence rate for coefficient functions which depend on path-suprema.
