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Preprints, Working Papers, ... Year : 2024

Nonparametric Estimation of the Transition Density Function for Diffusion Processes

Fabienne Comte
Nicolas Marie

Abstract

We assume that we observe $N$ independent copies of a diffusion process on a time interval $[0,2T]$. For a given time $t$, we estimate the transition density $p_t(x,y)$, namely the conditional density of $X_{t + s}$ given $X_s = x$, under conditions on the diffusion coefficients ensuring that this quantity exists. We use a least squares projection method on a product of finite dimensional spaces, prove risk bounds for the estimator and propose an anisotropic model selection method, relying on several reference norms. A simulation study illustrates the theoretical part for Ornstein-Uhlenbeck or square-root (Cox-Ingersoll-Ross) processes.
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Dates and versions

hal-04527294 , version 1 (29-03-2024)

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  • HAL Id : hal-04527294 , version 1

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Fabienne Comte, Nicolas Marie. Nonparametric Estimation of the Transition Density Function for Diffusion Processes. 2024. ⟨hal-04527294⟩
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