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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 94, 2022 - Issue 5
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Research Article

Solutions of semi-linear stochastic evolution integro-differential inclusions with Poisson jumps and non-local initial conditions

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Pages 647-679 | Received 21 Aug 2020, Accepted 02 Sep 2021, Published online: 23 Sep 2021
 

Abstract

In this paper, we mainly investigate properties on solution sets of a semi-linear stochastic evolution integro-differential inclusion with Poisson jumps and non-local initial conditions. We firstly establish the existence of solutions to the addressed equation via weak topology technique. Through establishing the estimate on noncompactness measure of integrals for Poisson jumps, we further show that the solution set is a compact Rδ-set when the resolvent operator is compact or non-compact, respectively.

Mathematics Subject Classification (2010):

Acknowledgements

Authors would like to thank the anonymous referee and the associate editor for carefully reading this manuscript and giving valuable comments to improve the previous version of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by NSF of Shaanxi Province of China [2020JM-183].

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