由分数Brown运动驱动的随机泛函微分方程的解的存在唯一性及平均原理

马丽; 常洪; 梁青

doi:10.21656/1000-0887.460078

由分数Brown运动驱动的随机泛函微分方程的解的存在唯一性及平均原理

doi: 10.21656/1000-0887.460078

海南师范大学数学与统计学院，海口 571158

基金项目:

海南省自然科学基金(124MS056)；海南省教育厅项目(Hnky2024-13)

详细信息

作者简介:
马丽(1979—),女，博士(E-mail: malihnsd@163.com)；常洪(2000—),男，硕士(E-mail: changhong8240@163.com)；梁青(1980—)，男，硕士(通信作者. E-mail: liangqing1112@sina.com).

通讯作者:
梁青(1980—)，男，硕士(通信作者. E-mail: liangqing1112@sina.com).

中图分类号: O211.63
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- 文章访问数: 12
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出版历程
- 收稿日期: 2025-04-15
- 修回日期: 2026-04-30
- 网络出版日期: 2026-06-04
- 刊出日期: 2026-05-01

Existence and Uniqueness With the Averaging Principle for Solutions to Stochastic Functional Differential Equations Driven by Fractional Brownian Motion

School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, P.R. China

摘要

摘要: 本文研究了由Hurst指数H>1/2的分数Brown运动和Lévy过程同时驱动的带Markov切换和随机比例时间的分布依赖的随机泛函微分方程.首先利用Carathédory逼近建立了方程解的存在唯一性，然后在一定的平均条件下，证明了分布依赖随机泛函微分方程的解被其平均化随机泛函微分方程的解在p-阶矩意义下逼近.
- 随机泛函微分方程 /
- 分数Brown运动 /
- Lévy过程 /
- 平均原理
Abstract: The distributiondependent stochastic functional differential equations, driven simultaneously by a fractional Brownian motion with Hurst index H>1/2 and a Lévy process and with the Markov switching and the random proportional times, were studied. Firstly, the existence and uniqueness of the solutions to the equations were established through the Carathédory approximation. Then, under certain averaging conditions, it is proved that the solution to the distributiondependent stochastic differential equation is approximated (in the sense of the p-th moment convergence) by the solution of its averaged stochastic functional differential equation.
- stochastic functional differential equation /
- fractional Brownian motion /
- Lévy process /
- averaging principle

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参考文献(14)

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[3]VAS’KOVSKII M M, STRYUK P P. Existence and uniqueness of strong solutions of mixed-type stochastic differential equations driven by fractional Brownian motions with Hurst exponents[J].Differential Equations,2024,60(6): 691-702.

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[14]〖JP2〗APPLEBAUM D.Lévy Processes and Stochastic Calculus[M]. 2nd ed. Cambridge: Cambridge University Press, 2009.

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由分数Brown运动驱动的随机泛函微分方程的解的存在唯一性及平均原理

doi: 10.21656/1000-0887.460078

作者简介:
马丽(1979—),女，博士(E-mail: malihnsd@163.com)；常洪(2000—),男，硕士(E-mail: changhong8240@163.com)；梁青(1980—)，男，硕士(通信作者. E-mail: liangqing1112@sina.com).

通讯作者:
梁青(1980—)，男，硕士(通信作者. E-mail: liangqing1112@sina.com).

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Existence and Uniqueness With the Averaging Principle for Solutions to Stochastic Functional Differential Equations Driven by Fractional Brownian Motion

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留言板

由分数Brown运动驱动的随机泛函微分方程的解的存在唯一性及平均原理

doi: 10.21656/1000-0887.460078

作者简介: 马丽(1979—),女，博士(E-mail: malihnsd@163.com)；常洪(2000—),男，硕士(E-mail: changhong8240@163.com)；梁青(1980—)，男，硕士(通信作者. E-mail: liangqing1112@sina.com).

通讯作者: 梁青(1980—)，男，硕士(通信作者. E-mail: liangqing1112@sina.com).

计量

出版历程

Existence and Uniqueness With the Averaging Principle for Solutions to Stochastic Functional Differential Equations Driven by Fractional Brownian Motion

计量

出版历程

目录

作者简介:
马丽(1979—),女，博士(E-mail: malihnsd@163.com)；常洪(2000—),男，硕士(E-mail: changhong8240@163.com)；梁青(1980—)，男，硕士(通信作者. E-mail: liangqing1112@sina.com).

通讯作者:
梁青(1980—)，男，硕士(通信作者. E-mail: liangqing1112@sina.com).