Exact Pathwise and Mean--Square Asymptotic Behaviour of Stochastic Affine Volterra and Functional Differential Equations

2013/10/09 by John A. D. Appleby, Appleby, John A. D., John A. Daniels +1
Economics, Econometrics and Finance · Mathematics · #Classical Analysis and ODEs (math.CA) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Differential Equations Analysis #Stochastic processes and financial applications #math.CA

paper · pdf · doi:10.48550/arxiv.1310.2337

37pp

arxiv created 2013/10/09 · openalex publication_date 2013/10/09 · arxiv updated 2013/10/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The almost sure rate of exponential-polynomial growth or decay of affine stochastic Volterra and affine stochastic finite-delay equations is investigated. These results are achieved under suitable smallness conditions on the intensities of the deterministic and stochastic perturbations diffusion, given that the asymptotic behaviour of the underlying deterministic resolvent is determined by the zeros of its characteristic equation. The results rely heavily upon a stochastic variant of the admissibility theory for linear Volterra operators.

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