Report
Nonparametric moment method for McKean-Vlasov stochastic differential equations
| العنوان: | Nonparametric moment method for McKean-Vlasov stochastic differential equations |
|---|---|
| المؤلفون: | Comte, Fabienne, Genon-Catalot, Valentine, Larédo, Catherine |
| المساهمون: | Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques (INSMI-CNRS)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire de Probabilités, Statistique et Modélisation (LPSM (UMR_8001)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité) |
| المصدر: | https://hal.science/hal-04460327 ; 2024. |
| بيانات النشر: | HAL CCSD |
| سنة النشر: | 2024 |
| مصطلحات موضوعية: | Invariant density, interaction function, Hermite basis, McKean-Vlasov stochastic differential equation, moment method, projection estimators, Nonparametric drift estimation, MSC 62G05-62M99-60J60, [STAT]Statistics [stat], [MATH]Mathematics [math] |
| الوصف: | We study the nonparametric estimation of both the potential and the interaction terms of a McKean-Vlasov stochastic differential equation (SDE) in stationary regime from a continuous observation on a time interval [0, T ], with asymptotic framework T → +∞. The problem is quite different from the case of usual diffusions with no interaction term and the observation of only one sample path is not enough to estimate both functions. We consider the observation of four i.i.d. sample paths. The observation of two sample paths could be enough at the cost of much more computations. Estimators of the potential and the interaction functions are built using a combination of a moment method and a projection method on sieves. We define a specific risk fitted to this estimation problem and obtain a bound for it. A nonparametric estimator of the invariant density also is proposed. The method is implemented on simulated data for several examples of McKean-Vlasov SDEs and a model selection procedure is experimented. |
| نوع الوثيقة: | report |
| اللغة: | English |
| Relation: | hal-04460327; https://hal.science/hal-04460327; https://hal.science/hal-04460327/document; https://hal.science/hal-04460327/file/NPMoments_26_01_24.pdf |
| الاتاحة: | https://hal.science/hal-04460327 https://hal.science/hal-04460327/document https://hal.science/hal-04460327/file/NPMoments_26_01_24.pdf |
| Rights: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.AECE6A81 |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |