非Lipschitz条件下带跳SDE数值方法的强收敛性

Convergence of the numerical method for SDE with Markovian switching and poisson jumps with non-Lipschitz coefficients

在随机微分方程数值方法的研究中为了避免一些Lipschitz条件的局限,在非Lips-chitz条件下,利用凹函数的性质,研究了具有马尔可夫调制的带Poisson跳的随机微分方程Euler-Maruyama方法的强收敛性,证明了数值解以1/2阶收敛到其精确解.

trader the study of the numerical methods for SDEs, avoiding the circumscribe of Lipschitz conditions, so the strong convergence of numerical methods for SDE with markovian switching and Poisson jumps with non-lipschitz coefficients is studied by using the properties of concave functions, and the convergence of the numerical approximation solution to the true solution with strong order p = 1/2 is showed.