圆柱非对称α-稳定Levy过程驱动的随机微分方程的极限分布

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Stochastics and Dynamics Pub Date : 2023-11-07 DOI:10.1142/s0219493723400063

Ting Li, Hongbo Fu, Xianming Liu

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引用次数: 0

摘要

研究一类非对称圆柱驱动的随机微分方程的极限分布[公式:见文]-稳定过程。在适当的条件下，证明了该方程的解弱收敛于Skorohod空间中布朗运动驱动的随机微分方程的解[公式:见文]。同时，得到了极限方程解的弱收敛速率，该速率依赖于[公式:见文]。为了说明，结果应用于一个简单的一维随机微分方程，这意味着弱收敛速度是最优的。

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

This paper deals with the limit distribution for a stochastic differential equation driven by a non-symmetric cylindrical [Formula: see text]-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 [Formula: see text]. Also, the rate of weak convergence, which depends on [Formula: see text], 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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来源期刊

Stochastics and Dynamics 数学-统计学与概率论

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This interdisciplinary journal is devoted to publishing high quality papers in modeling, analyzing, quantifying and predicting stochastic phenomena in science and engineering from a dynamical system''s point of view. Papers can be about theory, experiments, algorithms, numerical simulation and applications. Papers studying the dynamics of stochastic phenomena by means of random or stochastic ordinary, partial or functional differential equations or random mappings are particularly welcome, and so are studies of stochasticity in deterministic systems.