WIAS Preprint No. 680, (2001)

Transition density estimation for stochastic differential equations via forward-reverse representations


  • Milstein, Grigori N.
  • Schoenmakers, John G. M.
    ORCID: 0000-0002-4389-8266
  • Spokoiny, Vladimir
    ORCID: 0000-0002-2040-3427

2010 Mathematics Subject Classification

  • 62G07 60H10 65C05


  • transition density, forward and reverse diffusion, statistical estimation, Monte Carlo simulation




The general reverse diffusion equations are derived. They are applied to the problem of transition density estimation of diffusion processes between two fixed states. For this problem it is shown that density estimation based on forward-reverse representations allows for achieving essentially better results in comparison with usual kernel or projection estimation based on forward representations only.

Appeared in

  • Bernoulli, vol. 10(2), 2004, pp. 281--312

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