带泊松跳的中立型随机微积分方程的存在唯一性和稳定性(英文)

EXISTENCE, UNIQUENESS AND STABILITY OF NEUTRAL STOCHASTIC INTEGRODIFFERENTIAL EQUATIONS WITH POISSON JUMPS

本文研究了一类带泊松跳的中立型随机微积分方程(NSIDEPJs).利用Picard迭代法和Bihari不等式的一个推论,在一类广义利普希茨条件下获得了希尔伯特空间中NSIDEPJs温和解的存在唯一性和稳定性,改进和推广了已有的结果.最后,举例说明本文结果的有效性.

In this paper, we study a class of neutral stochastic integrodifferential equations with Poisson jumps （NSIDEPJs）. By using the method of Picard approximation and a corollary of Bihari＇s inequality, we obtain the existence, uniqueness and stability of mild solutions for NSIDEPJs under a class of generalized Lipschitz condition in a Hilbert space, which generalize and improve some known results. Finally, an example is provided to illustrate the efficiency of the obtained results.