带有泊松跳跃马尔可夫调制的中立型随机时滞微分方程近似解的依概率收敛

Convergence in Probability of Approximate Solutions for Neutral Stochastic Differential Delay Equations with Poisson Jumps and Markovian Switching

摘要: 本文在局部Lipschitz条件和一些附加条件下得到了方程的全局解, 而未使用线性增长条件. 另外, 对带有泊松跳跃马尔可夫调制的中立型随机时滞微分方程近似解的收敛性进行了研究, 取代了以往的均方收敛方式, 改为依概率收敛. 从而对现有的一些结果进行了改进.

Abstract: In the paper, a global solution is guaranteed under local Lipschitz condition and some additional conditions without linear growth condition. Later, the convergence in probability of approximate solutions is investigated on the neutral stochastic differential delay equations with Poisson jumps and Markovian switching, instead of L^2. Some known results are generalized and improved.