数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (3): 876-886.doi: 10.1007/s10473-022-0304-8

• 论文 • 上一篇    下一篇

PARAMETER ESTIMATION OF PATH-DEPENDENT MCKEAN-VLASOV STOCHASTIC DIFFERENTIAL EQUATIONS

刘美琪1, 乔会杰1,2   

  1. 1. Department of Mathematics, Southeast University, Nanjing, 211189, China;
    2. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA
  • 收稿日期:2020-10-13 修回日期:2021-06-14 发布日期:2022-06-24
  • 通讯作者: Huijie QIAO,E-mail:hjqiaogean@seu.edu.cn E-mail:hjqiaogean@seu.edu.cn
  • 基金资助:
    The second author is supported by NSF of China (11001051, 11371352, 12071071) and China Scholarship Council (201906095034).

PARAMETER ESTIMATION OF PATH-DEPENDENT MCKEAN-VLASOV STOCHASTIC DIFFERENTIAL EQUATIONS

Meiqi LIU1, Huijie QIAO1,2   

  1. 1. Department of Mathematics, Southeast University, Nanjing, 211189, China;
    2. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA
  • Received:2020-10-13 Revised:2021-06-14 Published:2022-06-24
  • Contact: Huijie QIAO,E-mail:hjqiaogean@seu.edu.cn E-mail:hjqiaogean@seu.edu.cn
  • Supported by:
    The second author is supported by NSF of China (11001051, 11371352, 12071071) and China Scholarship Council (201906095034).

摘要: This work concerns a class of path-dependent McKean-Vlasov stochastic differential equations with unknown parameters. First, we prove the existence and uniqueness of these equations under non-Lipschitz conditions. Second, we construct maximum likelihood estimators of these parameters and then discuss their strong consistency. Third, a numerical simulation method for the class of path-dependent McKean-Vlasov stochastic differential equations is offered. Finally, we estimate the errors between solutions of these equations and that of their numerical equations.

关键词: Path-dependent McKean-Vlasov stochastic differential equations, maximum likelihood estimation, the strong consistency, numerical simulation

Abstract: This work concerns a class of path-dependent McKean-Vlasov stochastic differential equations with unknown parameters. First, we prove the existence and uniqueness of these equations under non-Lipschitz conditions. Second, we construct maximum likelihood estimators of these parameters and then discuss their strong consistency. Third, a numerical simulation method for the class of path-dependent McKean-Vlasov stochastic differential equations is offered. Finally, we estimate the errors between solutions of these equations and that of their numerical equations.

Key words: Path-dependent McKean-Vlasov stochastic differential equations, maximum likelihood estimation, the strong consistency, numerical simulation

中图分类号: 

  • 60H10