一类带Lévy噪声的随机McKean-Vlasov方程的参数估计问题

doi:10.6040/j.issn.1671-9352.0.2024.126

《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (5): 107-115.doi: 10.6040/j.issn.1671-9352.0.2024.126

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一类带Lévy噪声的随机McKean-Vlasov方程的参数估计问题

冯春宇,吕艳^*

南京理工大学数学与统计学院, 江苏南京 210094

发布日期:2025-05-19
通讯作者: 吕艳(1981— ),女,教授,博士生导师,博士,研究方向为随机偏微分方程的动力行为. E-mail:lvyan1998@aliyun.com
作者简介:冯春宇(1998— ),女,硕士研究生,研究方向为随机偏微分方程的参数估计. E-mail:chunkyfung@163.com*通信作者:吕艳(1981— ),女,教授,博士生导师,博士,研究方向为随机偏微分方程的动力行为. E-mail:lvyan1998@aliyun.com
基金资助:
国家自然科学基金资助项目(12371243)

Parameter estimation for a class of McKean-Vlasov stochastic differential equation with Lévy noise

FENG Chunyu, LYU Yan^*

School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China

Published:2025-05-19

摘要/Abstract

摘要： 建立了一类带Lévy噪声的随机McKean-Vlasov方程和其对应的相互作用粒子系统的参数估计之间在平均极限下的关系。给出简单的平均场极限结果,即相互作用粒子系统的解在L²(Ω)意义下的收敛。得到了两系统中未知参数的极大似然估计(＾overθ)^N和(-overθ),并证明当N趋向无穷大时,(＾overθ)^N依概率收敛到(-overθ)。

关键词: McKean-Vlasov方程, 相互作用粒子系统, 极大似然估计, It(＾overo)公式

Abstract: A relationship between parameter estimators of a class of stochastic McKean-Vlasov equations with Lévy noise and their corresponding interacting particle systems is established. The simple mean field limit result is given, that is, the convergence of the solution of the interacting particle system in the sense of L2(Ω). The maximum likelihood estimators of unknown parameters (＾overθ)^N and (-overθ) in the two systems are constructed. We show that when N tends to infinity, (＾overθ)^N converges to (-overθ)in probability.

Key words: McKean-Vlasov equations, interacting particle system, maximum likelihood estmation, It(＾overo)formula

中图分类号:

O211.63

冯春宇,吕艳. 一类带Lévy噪声的随机McKean-Vlasov方程的参数估计问题[J]. 《山东大学学报(理学版)》, 2025, 60(5): 107-115.

FENG Chunyu, LYU Yan. Parameter estimation for a class of McKean-Vlasov stochastic differential equation with Lévy noise[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(5): 107-115.

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一类带Lévy噪声的随机McKean-Vlasov方程的参数估计问题

Parameter estimation for a class of McKean-Vlasov stochastic differential equation with Lévy noise

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