# S2γ -WPAA FUNCTIONS AND APPLICATIONS TO STOCHASTIC NEUTRAL FUNCTIONAL EQUATIONS WITH INFINITE DELAY

 Title S2γ -WPAA FUNCTIONS AND APPLICATIONS TO STOCHASTIC NEUTRAL FUNCTIONAL EQUATIONS WITH INFINITE DELAY Publication Type Journal Article Year of Publication 2018 Authors TANG CHAO, CHANG YONG-KUI Journal Dynamic Systems and Applications Volume 27 Issue 3 Start Page 495 Pagination 36 Date Published 2018 ISSN 1056-2176 AMS Subject Classification 34C27, 34D20, 34F05, 60H30 Abstract In this paper, we introduce the concept of ${ S^2_{\gamma} }$ -weighted pseudo almost automorphy. And then, we investigate some basic properties such as completeness of spaces, ergodic and composition theorems of such stochastic processes. Finally, by virtue of theories of evolution systems, fading phase spaces for infinite delay and the stochastic analysis techniques, we apply the results obtained to consider the existence and uniqueness results of weighted pseudo almost automorphic solutions in distribution to a class of nonautonomous stochastic neutral functional equations with infinite delay under ${ S^2_{\gamma} }$ -weighted pseudo almost automorphic coefficients in real separable Hilbert spaces. PDF https://acadsol.eu/dsa/articles/27/3/4.pdf DOI 10.12732/dsa.v27i3.4 Refereed Designation Refereed Full Text REFERENCES [1] S. Abbas, Existence and attractivity of k-pseudo almost automorphic sequence solution of a model of bidirectional neural networks, Acta Appl. Math., 119 (2012), 57-74. [2] P. Bezandry, T. Diagana, Almost Periodic Stochastic Processes, Springer, New York, (2011). [3] J. Blot, P. Cieutat, K. 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