Towards a Characterization of Markov Processes Enjoying the Time-Inversion Property |
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Authors: | Stephan Lawi |
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Institution: | (1) Laboratoire de Probabilités et Modèles Aléatoires, CNRS-UMR 7599, Université Paris VI & Université Paris VII, 4 Place Jussieu, 75252 Paris Cedex 05, France |
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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 (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.
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Keywords: | Homogeneous Markov processes Time-inversion property Bessel processes Dunkl processes Wishart processes Semi-stable processes |
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