EXISTENCE OF ALMOST AUTOMORPHIC SOLUTION IN DISTRIBUTION FOR A CLASS OF
STOCHASTIC INTEGRO-DIFFERENTIAL EQUATION DRIVEN BY LEVY NOISE
Abstract
We investigate a new class of stochastic integro-differential equations
driven by L´evy noise. Particularly, based on Schauder’s fixed point
theorem, the existence of square-mean almost automorphic mild solution
in distribution is obtained by using some conditions which are weaker
than Lipschitz conditions. Our result can be seen as a generalisation of
the result of [17] and [28] based on the compactness of solution
semigroup operators of our slightly different stochastic model. We
provide an example to illustrate ours results.