Conţinutul numărului revistei |
Articolul precedent |
Articolul urmator |
447 0 |
SM ISO690:2012 CHEBAN, David, LIU, Zhenxin. Periodic, quasi-periodic, almost periodic, almost automorphic, Birkhoff recurrent and Poisson stable solutions for stochastic differential equations. In: Journal of Difference Equations and Applications, 2020, nr. 4(269), pp. 3652-3685. ISSN 0022-6198. DOI: https://doi.org/10.1016/j.jde.2020.03.014 |
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Journal of Difference Equations and Applications | ||||||
Numărul 4(269) / 2020 / ISSN 0022-6198 /ISSNe 1090-2732 | ||||||
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DOI:https://doi.org/10.1016/j.jde.2020.03.014 | ||||||
Pag. 3652-3685 | ||||||
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Rezumat | ||||||
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. |
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Cuvinte-cheie Almost automorphic solution, asymptotic stability, Birkhoff recurrent solution, Bohr/Levitan almost periodic solution, Poisson stable solution, quasi-periodic solution, Stochastic differential equation |
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