On the limit distribution for stochastic differential equations driven by cylindrical non-symmetric α-stable Lévy processes

2023/02/17 by Ting Li, Li, Ting, Hongbo Fu +3
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2302.08693

openalex publication_date 2023/02/17 · openalex created_date 2023/02/21 · openalex updated_date 2026/07/28

Abstract

This article deals with the limit distribution for a stochastic differential equation driven by a non-symmetric cylindrical α-stable process. Under suitable conditions, it is proved that the solution of this equation converges weakly to that of a stochastic differential equation driven by a Brownian motion in the Skorohod space as α→2. Also, the rate of weak convergence, which depends on 2-α, for the solution towards the solution of the limit equation is obtained. For illustration, the results are applied to a simple one-dimensional stochastic differential equation, which implies the rate of weak convergence is optimal.

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