随机泛函微分方程参数估计的渐近行为

数学物理学报 ›› 2024, Vol. 44 ›› Issue (3): 746-760.

随机泛函微分方程参数估计的渐近行为

王佳曦(),毛明志^*()

中国地质大学(武汉)数理学院武汉 430074

收稿日期:2023-04-24 修回日期:2023-12-04 出版日期:2024-06-26 发布日期:2024-05-17
通讯作者: *毛明志，E-mail：mingzhi-mao@cug.edu.cn
作者简介:王佳曦，E-mail：1065378050@qq.com
基金资助:
中国地质大学(武汉)基础数学研究中心基金

The Asymptotic Behaviors for Parameter Estimation of Stochastic Functional Differential Equations

Wang Jiaxi(),Mao Mingzhi^*()

School of Mathematics and Physics, China University of Geosciences, Wuhan 430074

Received:2023-04-24 Revised:2023-12-04 Online:2024-06-26 Published:2024-05-17
Supported by:
FRFC(CUGSX01)

摘要/Abstract

摘要：

该文主要研究一类分布依赖随机泛函微分方程（McKean-Vlasov SDE）的系数最小距离估计值问题. 在漂移系数满足一定假设条件下, 得到了估计量的极限分布, 进而讨论估计量的相合性和渐近正态性, 在 $ L^\gamma $ 惩罚函数约束条件下, 该文也给出了系数估计量的渐近行为, 一个典型例子.

关键词: Wasserstein度量, 最小距离估计, Gronwall不等式, 分布测度

Abstract:

This paper studies the minimum distance estimate for stochastic functional differential equations (McKean-Vlasov SDE). Under some assumptions for the drift coefficient, it obtains the consistency and the limit distribution on the estimators as the diffusion coefficient goes to zero. Further, it also discusses the asymptotic behavior of the coefficient estimators under the condition of the $ L^\gamma $ penalty function. A typical case is provided.

Key words: Wasserstein metric, Minimum distance estimation, Gronwall's inequality, Distribution measure

中图分类号:

O211.4

王佳曦, 毛明志. 随机泛函微分方程参数估计的渐近行为[J]. 数学物理学报, 2024, 44(3): 746-760.

Wang Jiaxi, Mao Mingzhi. The Asymptotic Behaviors for Parameter Estimation of Stochastic Functional Differential Equations[J]. Acta mathematica scientia,Series A, 2024, 44(3): 746-760.

参考文献 16

[1]	Amorino C, Heidari A, Picipauskaitè V, Podolskij M. Parameter estimation of discretely observed interacting particle systems. Stoch Process Appl, 2023, 163(2): 350-386
[2]	Bressloff P C. Stochastic Processes in Cell Biology. New York: Springer, 2014
[3]	Carmona R, Delarue F. Probabilistic Theory of Mean Field Games with Applications I, Mean Field FBSDEs, Control and Games. New York: Springer, 2018
[4]	Dos Reis G, Salkekd K, Tugaut J. Freidlin Wentzell LDP in path space for Mckean Vlasov equations and the functional iterated logarithm law. Ann Appl Probab, 2019, 29(3): 1487-1540
[5]	Genon-Catalot V, Larédo C. Parametric inference for small variance and long time horizon McKean-Vlasov diffusion models. Electr J Statist, 2021, 15: 5811-5854
[6]	Gregorio A D, Iacus S M. On penalized estimation for dynamical systems with small noise. Elect J Statist, 2018, 12: 1614-1630
[7]	Herrmann S, Imkeller P, Peithmann D. Large deviations and a Kramers'type law for self-stabilizing diffusions. Ann Appl Probab, 2008, 18: 1379-1423
[8]	Knight K, Fu W. Asymptotics for lasso-type estimators. Ann Statist, 2000, 5(28): 1536-1578
[9]	Kutoyants Y, Pilibossian P. On minimum uniform metric estimate of parameters of diffusion-type processes. Stoch Process Appl, 1994, 51(2): 259-267
[10]	Maestra L D, Hoffmann M. The LAN property for Mckean-Vlasov models in a mean-field regime. Stoch Process Appl, 2023, 155(1): 109-146
[11]	Nkurunziza S, Ahmed S. Shrinkage drift parameter estimation for multi-factor Ornstein-Uhlenbeck processes. Appl Stoch Models Bus Ind, 2010, 26: 103-124
[12]	Ren P, Wang F. Bismut formula for lions derivative of distribution dependent SDEs and applications. J Diff Equ, 2019, 267(8): 4745-4777
[13]	Ren P, Wu J. Least squeres estimation for path-distribution McKean-Vlasov SDEs via discrete-time observations. Acta Math Sci, 2019, 39B(3): 691-716
[14]	Sharrock L, Kantas N, Parpas P, Pavliotis G A. Online parameter estimation for the McKean-Vlasov stochastic differential equation. Stoch Process Appl, 2023, 162(2): 481-546
[15]	Takahashi A. An asymptotic expansion approach to pricing financial contingent claims. Asia-Pacific Financ Markets, 1999, 6(2): 115-151
[16]	Zhao H, Zhang C. Minimum distance parameter estimation for SDEs with small $ \alpha $-stable noises. Statist Probab Lett, 2019, 145: 301-311