Indexed by:
Journal Papers
First Author:
Cheban, David
Correspondence Author:
Liu, ZX (reprint author), Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China.
Co-author:
Liu, Zhenxin
Date of Publication:
2020-08-05
Journal:
JOURNAL OF DIFFERENTIAL EQUATIONS
Included Journals:
SCIE
Document Type:
J
Volume:
269
Issue:
4
Page Number:
3652-3685
ISSN No.:
0022-0396
Key Words:
Stochastic differential equation; Quasi-periodic solution; Bohr/Levitan
almost periodic solution; Almost automorphic solution; Birkhoff
recurrent solution; Poisson stable solution; Asymptotic stability
Abstract:
The paper is dedicated to studying the problem of Poisson stability (in particular stationarity, periodicity, quasi-periodicity, Bohr almost periodicity, Bohr almost automorphy, Birkhoff recurrence, almost recurrence in the sense of Bebutov, Levitan almost periodicity, pseudo-periodicity, pseudo-recurrence, Poisson stability) of solutions for semi-linear stochastic equation
dx(t) = (Ax(t) + f(t, x(t)))dt + g(t, x(t))dW(t) (*)
with exponentially stable linear operator A and Poisson stable in time coefficients f and g. We prove that if the functions f and g are appropriately "small", then equation (*) admits at least one solution which has the same character of recurrence as the functions f and g. We also discuss the asymptotic stability of these Poisson stable solutions. (C) 2020 Elsevier Inc. All rights reserved.
Translation or Not:
no
