EXISTENCE AND STABILITY OF SOLUTIONS OF NEUTRAL HYBRID STOCHASTIC INFINITE DELAY DIFFERENTIAL EQUATIONS WITH POISSON JUMPS

Abstract

In this paper, we prove the existence, uniqueness and stability of solutions of neutral stochastic innite delay dierential equations with Poisson jumps and Markovian switching in the phase space BC( (-\infty,0];R^d ) which is the family of bounded continuous R^d -valued functions \varphi dfined on (-\infty, 0] with norm ||\varphi||=sup _{-\infty < \theta <= 0} | \varphi (\theta)| under non-Lipschitz condition and weakened linear growth condition. The solutions are constructed by the successive approximation method. Also we prove the continuous dependence of solutions on the initial value.