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Towards a Characterization of Markov Processes Enjoying the Time-Inversion Property

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  • Stephan Lawi

    (Université Paris VI & Université Paris VII)

Abstract

We give a necessary and sufficient condition for a homogeneous Markov process taking values in ℝ n to enjoy the time-inversion property of degree α. The condition sets the shape for the semigroup densities of the process and allows to further extend the class of known processes satisfying the time-inversion property. As an application we recover the result of Watanabe (Z. Wahrscheinlichkeitstheor. Verwandte Geb. 31:115–124, 1975) for continuous and conservative Markov processes on ℝ+. As new examples we generalize Dunkl processes and construct a matrix-valued process with jumps related to the Wishart process by a skew-product representation.

Suggested Citation

  • Stephan Lawi, 2008. "Towards a Characterization of Markov Processes Enjoying the Time-Inversion Property," Journal of Theoretical Probability, Springer, vol. 21(1), pages 144-168, March.
    • Handle: RePEc:spr:jotpro:v:21:y:2008:i:1:d:10.1007_s10959-007-0104-z
    DOI: 10.1007/s10959-007-0104-z
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    References listed on IDEAS

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    1. Bru, Marie-France, 1989. "Diffusions of perturbed principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 29(1), pages 127-136, April.
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