Infinite-delayed stochastic impulsive differential systems with Poisson jumps

This manuscript investigates a broad class of stochastic differential equation steered by Poisson jumps and impulses in a Hilbert space. We use successive approximation method to show the existence of a solution. The continuous dependence of the solutions to the initial data is also studied. Finally, the existence of optimal state-control pair for the associated Lagrangian problem is discussed. An example is also presented to validate the theoretical results.

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