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.

Automated summary

This manuscript investigates a class of stochastic differential equations in a Hilbert space steered by Poisson jumps and impulses, using the successive approximation method to prove the existence of a solution and studying the continuous dependence of solutions on initial data. The existence of optimal state-control pairs for the associated Lagrangian problem is also discussed, with an example provided to validate the theoretical results.