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EXISTENCE OF ALMOST AUTOMORPHIC SOLUTION IN DISTRIBUTION FOR A CLASS OF STOCHASTIC INTEGRO-DIFFERENTIAL EQUATION DRIVEN BY LÉVY NOISE
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EXISTENCE OF ALMOST AUTOMORPHIC SOLUTION IN DISTRIBUTION FOR A CLASS OF STOCHASTIC INTEGRO-DIFFERENTIAL EQUATION DRIVEN BY LÉVY NOISE

Mamadou Moustapha Mbaye and Solym Manou-Abi

Abstract

We investigate a class of stochastic integro-differential equations driven by Lévy noise. Under some appropriate assumptions, we establish the existence of an square-mean almost automorphic solutions in distribution. Particularly, based on Schauder's fixed point theorem, the existence of square-mean almost automorphic mild solution distribution is obtained by using the condition which is weaker than Lipschitz conditions. We provide an example to illustrate ours results.
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