一类带跳的随机比例微分方程解的存在唯一性和Euler数值方法的收敛性

Convergence of Euler Methods for Stochastic Pantograph Equations with Jumps

本文主要研究了下列带跳的随机比例微分方程:{dX(t)=f(X(t),X(qt))dt+g(X(t),X(gt))dW(t)+∫_(Rn)h(X(t),X(qt),u)(?)(dt,du),0≤t≤T,X(0)=X_0.我们首先给出此方程的解存在且唯一;在此基础上给出了Euler方法的数值解,证明了数值解L^2意义下收敛于精确解.

In this paper, the authors mainly study the following stochastic pantograph equations with jumps：{dX（t）=f（X（t）,X（qt））dt＋g（X（t）,X（qt））dW（t）＋∫R^nh（X（f）,X（qt）,u）N^-（dt,du）,0≤t≤T, X（0）=X0.Firstly, the existence and uniqueness of the solution to the equation under some coefficient related conditions are proved. Based on this, numerical solution to the Euler method is provided by the authors. At last, it is proved that, the numerical solution is convergent to the analytical solution in L^2 .