Convergence rate of stability problems of SDEs with (dis-)continuous coefficients

2014/01/18 by Hashimoto Hashimoto, Hashimoto, Hashimoto, Takahiro Tsuchiya +1
Computer Science · Economics, Econometrics and Finance · Engineering · Mathematics · #41A25 #60H10 #60H35 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #math.PR #msc:41A25 #msc:60H10 #msc:60H35

paper · pdf · doi:10.48550/arxiv.1401.4542

Revised argument in $L^p$-estimation

openalex publication_date 2014/01/18 · arxiv created 2014/04/02 · arxiv updated 2014/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the stability problems of one dimensional SDEs when the diffusion coefficients satisfy the so called Nakao-Le Gall condition. The explicit rate of convergence of the stability problems are given by the Yamada-Watanabe method without the drifts. We also discuss the convergence rate for the SDEs driven by the symmetric α stable process. These stability rate problems are extended to the case where the drift coefficients are bounded and in L¹. It is shown that the convergence rate is invariant under the removal of drift method for the SDEs driven by the Wiener process.

Related

• Convergence rate of numerical scheme for SDEs with a distributional drift in Besov space
• L^α-1 distance between two one-dimensional stochastic differential equations with drift terms driven by a symmetric α-stable process
• Distribution Dependent SDEs with Hölder Continuous Drift and α-Stable Noise
• Strong rate of convergence for the Euler-Maruyama approximation of SDEs with Hölder continuous drift coefficient
• Probability density function of SDEs with unbounded and path--dependent drift coefficient