6533b7d5fe1ef96bd126470a
RESEARCH PRODUCT
A Criterium for the Strict Positivity of the Density of the Law of a Poisson Process
Rémi Léandresubject
Algebra and Number TheorySemigroupStochastic processlcsh:MathematicsApplied MathematicsMarkov processlcsh:QA1-939Malliavin calculussymbols.namesakeLawCompound Poisson processJumpsymbolsFinite setJump processAnalysisMathematicsdescription
We translate in semigroup theory our result (Leandre, 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 to the end point if the density of the jump process is strictly positive in . We use the Malliavin Calculus of Bismut type of (Leandre, (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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-01-01 | Advances in Difference Equations |