Approximate maximum likelihood estimation for stochastic differential equations with random effects in the drift and the diffusion - Archive ouverte HAL Access content directly
Journal Articles Metrika Year : 2018

Approximate maximum likelihood estimation for stochastic differential equations with random effects in the drift and the diffusion

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Abstract

Consider N independent stochastic processes (Xi (t), t. [ 0, T]), i = 1,..., N, defined by a stochastic differential equation with random effects where the drift term depends linearly on a random vector Phi i and the diffusion coefficient depends on another linear random effect Psi i. For these effects, we consider a joint parametric distribution. We propose and study two approximate likelihoods for estimating the parameters of this joint distribution based on discrete observations of the processes on a fixed time interval. Consistent and v N-asymptotically Gaussian estimators are obtained when both the number of individuals and the number of observations per individual tend to infinity. The estimation methods are investigated on simulated data and show good performances.
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Dates and versions

hal-02621496 , version 1 (26-05-2020)

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Maud Delattre, Valentine Genon-Catalot, Catherine Laredo. Approximate maximum likelihood estimation for stochastic differential equations with random effects in the drift and the diffusion. Metrika, 2018, 81 (4), pp.953-983. ⟨10.1007/s00184-018-0666-z⟩. ⟨hal-02621496⟩
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