Nonparametric estimation of the transition density function for diffusion processes

Fabienne Comte and Nicolas Marie

Stochastic Processes and their Applications, 2025, vol. 188, issue C

Abstract: We assume that we observe N∈N∗ independent copies of a diffusion process on a time-interval [0,2T]. For a given time t∈(0,T], we estimate the transition density pt(x,.), namely the conditional density of Xt+s given Xs=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.

Date: 2025
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DOI: 10.1016/j.spa.2025.104667

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