Nonparametric Estimation of the Transition Density Function for Diffusion Processes

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.

32 pages, 5 figures

References in corpus (8)

• Concentration around the mean for maxima of empirical processes
• Nonparametric estimation for interacting particle systems : McKean-Vlasov models
• Nonparametric estimation of the stationary density and the transition density of a Markov chain
• Nadaraya-Watson Estimator for I.I.D. Paths of Diffusion Processes
• Nonparametric Estimation for I.I.D. Paths of a Martingale Driven Model with Application to Non-Autonomous Financial Models
• On a Computable Skorokhod's Integral Based Estimator of the Drift Parameter in Fractional SDE
• On a Projection Least Squares Estimator for Jump Diffusion Processes
• Adaptive nonparametric estimation in the functional linear model with functional output