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Pinned Diffusions and Markov Bridges

Author

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  • Florian Hildebrandt

    (University of Hamburg)

  • Sylvie Rœlly

    (Institut für Mathematik der Universität Potsdam)

Abstract

In this article, we consider a family of real-valued diffusion processes on the time interval [0, 1] indexed by their prescribed initial value $$x \in \mathbb {R}$$x∈R and another point in space, $$y \in \mathbb {R}$$y∈R. We first present an easy-to-check condition on their drift and diffusion coefficients ensuring that the diffusion is pinned in y at time $$t=1$$t=1. Our main result then concerns the following question: can this family of pinned diffusions be obtained as the bridges either of a Gaussian Markov process or of an Itô diffusion? We eventually illustrate our precise answer with several examples.

Suggested Citation

  • Florian Hildebrandt & Sylvie Rœlly, 2020. "Pinned Diffusions and Markov Bridges," Journal of Theoretical Probability, Springer, vol. 33(2), pages 906-917, June.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:2:d:10.1007_s10959-019-00954-5
    DOI: 10.1007/s10959-019-00954-5
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    References listed on IDEAS

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    1. Brennan, Michael J & Schwartz, Eduardo S, 1990. "Arbitrage in Stock Index Futures," The Journal of Business, University of Chicago Press, vol. 63(1), pages 7-31, January.
    2. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, January.
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    Cited by:

    1. Abel Azze & Bernardo D'Auria & Eduardo Garc'ia-Portugu'es, 2022. "Optimal stopping of Gauss-Markov bridges," Papers 2211.05835, arXiv.org, revised Jul 2024.

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