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Bounds for the transition density of time-homogeneous diffusion processes

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  • Downes, A.N.

Abstract

The paper presents new simple sharp bounds for transition density functions for time-homogeneous diffusion processes. The bounds are obtained under mild conditions on the drift and diffusion coefficients, extending and substantially improving previous results in the literature which were limited to drifts satisfying a linear growth condition. They lead to an asymptotic expression for the time t transition density as t-->0. While the focus is on the one-dimensional case, an extension to multiple dimensions is discussed. Results are illustrated by numerical examples.

Suggested Citation

  • Downes, A.N., 2009. "Bounds for the transition density of time-homogeneous diffusion processes," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 835-841, March.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:6:p:835-841
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    References listed on IDEAS

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    1. Qian, Zhongmin & Zheng, Weian, 2004. "A representation formula for transition probability densities of diffusions and applications," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 57-76, May.
    2. Andrew N. Downes & Konstantin Borovkov, 2008. "First Passage Densities and Boundary Crossing Probabilities for Diffusion Processes," Methodology and Computing in Applied Probability, Springer, vol. 10(4), pages 621-644, December.
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    Cited by:

    1. Kirkby, J.L. & Nguyen, Dang H. & Nguyen, Duy & Nguyen, Nhu N., 2022. "Maximum likelihood estimation of diffusions by continuous time Markov chain," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).

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