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

doi:10.1007/s10473-022-0304-8

Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (3): 876-886.doi: 10.1007/s10473-022-0304-8

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

Meiqi LIU¹, Huijie QIAO^1,2

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 Online:2022-06-26 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).

Abstract

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

CLC Number:

60H10

Meiqi LIU, Huijie QIAO. PARAMETER ESTIMATION OF PATH-DEPENDENT MCKEAN-VLASOV STOCHASTIC DIFFERENTIAL EQUATIONS[J].Acta mathematica scientia,Series A, 2022, 42(3): 876-886.

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

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