Caputo fractional stochastic differential equations: Lipschitz continuity in the fractional order

2024/12/28 by Ta Cong Son, Son, T. C., Nguyễn Tiến Dũng +9 · 1 citation
Economics, Econometrics and Finance · Mathematics · #26A33 #60H07 #60J70 #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2412.19965

openalex publication_date 2024/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider a class of the Caputo fractional stochastic differential equations of fractional order α∈ ((1)/(2),1]. Our aim is to analyze of the continuous dependence of solutions on the fractional order α. We first provide explicit estimates for the rate of weak convergence the solutions. We then describe the exact asymptotic behavior of this convergence to show that the rate is optimal.

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• A Conjugate Gradient Method for Nonlinear Programming Problems using Caputo Fractional Gradients

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