A Criterium for the Strict Positivity of the Density of the Law of a Poisson Process
نویسنده
چکیده
We translate in semigroup theory our result Léandre, 1990 giving a necessary condition so that the law of a Markov process with jumps could have a strictly positive density. This result express, that we have to jump in a finite number of jumps in a “submersive” way from the starting point x to the end point y if the density of the jump process p1 x, z is strictly positive in x, y . We use theMalliavin Calculus of Bismut type of Léandre, 2008;2010 translated in semi-group theory as a tool, and the interpretation in semi-group theory of some classical results of the stochastic analysis for Poisson process as, for instance, the formula giving the law of a compound Poisson process.
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