Existence of Periodic Solutions in Distribution for Stochastic Newtonian Systems

Periodic solutions in distribution of stochastic lattice differential equations

“…This contradicts (25). Thus, equality (24) holds. Then for all s ∈ [τ y i , ρ y i ], n > Ñ2 , we have b i,n (s) ≤ 0 on U.…”

“…It is thought to be a challenging topic to investigate periodic behavior of stochastic dynamical systems. Some can be found in [8,13,27,28,29,32] for almost periodic solutions, almost automorphic solutions and quasi-periodic solutions, [15,16,41] for pathwise random periodic solutions and pathwise quasi-periodic solutions, and [8,9,13,20,21,22,23,24] for periodic solutions in distribution.…”