Nonparametric estimation of the transition density function for diffusion processes
Year: 2025
Type: article
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.
Authors: Fabienne Comte, Nicolas Marie
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: hybrid
Estimated APC paid: $3,520
OpenAlex ID: W4409839160