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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