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Nonparametric estimation of the transition density function for diffusion processes

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  • Comte, Fabienne
  • Marie, Nicolas

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.

Suggested Citation

  • Comte, Fabienne & Marie, Nicolas, 2025. "Nonparametric estimation of the transition density function for diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:spapps:v:188:y:2025:i:c:s0304414925001085
    DOI: 10.1016/j.spa.2025.104667
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