Accepted for publication in JNEEA: Ms #2406031

Almost Periodic Solutions of Stochastic Singular Difference Equations


P. H. Bezandry

Department of Mathematics, Howard University, Washington DC 20059

Received on June 2, 2024, revised version on December 13, 2024
Accepted on January 7, 2024

Communicated by Mamadou Moustapha MBAYE

Abstract.  In this paper we study and obtain the existence of almost periodic solutions of the following class of stochastic singular difference equations of the form:
A X(k + 1) + B X(k) = f(k, X(k)) ξ(k + 1), k ∈ ℤ,
where A and B are singular N × N random matrices (det A = det B = 0),   f : ℤ × L1(Ω; ℝN) → L1(Ω; ℝN)   is almost periodic in the first variable uniformly in the second one, and ξ = { ξ(k), k ∈ ℤ } is an almost periodic random sequence and stochastically independent of f. These results are, subsequently, applied to find the existence of almost periodic solutions of the second-order stochastic singular difference equations.
Keywords: almost periodic sequence, stochastic difference equation, singular random matrix.
2010 Mathematics Subject Classification:   Primary 39A10, 60H10; Secondary 34F05.

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