Towards a characterization of Markov processes enjoying the time-inversion property

Stephan Lawi

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Towards a characterization of Markov processes enjoying the time-inversion property

Stephan Lawi

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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 in \cite{Wa1975} 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.

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Stephan Lawi. 2007-04-26. Towards a characterization of Markov processes enjoying the time-inversion property. https://arxiv.org/abs/math/0506013

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