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Inference for ergodic McKean-Vlasov stochastic differential equations with polynomial interactions
Genon-Catalot, Valentine
Laredo, Catherine
Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145) ; Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)
hal-03866218
https://cnrs.hal.science/hal-03866218
https://cnrs.hal.science/hal-03866218v2/document
https://cnrs.hal.science/hal-03866218v2/file/AIHP2204-003_Revision_Genon_Laredo.pdf
https://cnrs.hal.science/hal-03866218
2022
en
Parametric inference
Invariant distribution
Asymptotic properties of estimators
Approximate likelihood
Long time asymptotics
MSC2020 subject classifications: Primary 60J60
60J99
62F12
62M05 McKean-Vlasov stochastic differential equation
Continuous observations
[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]
info:eu-repo/semantics/preprint
Preprints, Working Papers, ...
We consider a specific family of one-dimensional McKean-Vlasov stochastic differential equations with no potential term and with interaction term modeled by an odd increasing polynomial. We assume that the observed process is in stationary regime and that the sample path is continuously observed on a time interval [0, 2T ]. Due to the McKean-Vlasov structure, the drift function depends on the unknown marginal law of the process in addition to the unknown parameters present in the interaction function. This is why the exact likelihood function does not lead to computable estimators. We overcome this difficulty by a two-step approach leading to an approximate likelihood function. We then derive explicit estimators of the coefficients of the interaction term and prove their consistency and asymptotic normality with rate √ T as T grows to infinity. Examples illustrating the theory are proposed.
2022-11-22
info:eu-repo/semantics/OpenAccess