Some Relations Between Bounded Below Elliptic Operators and Stochastic Analysis

  • Rémi LéandreEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 303)


We apply Malliavin Calculus tools to the case of a bounded below elliptic right-invariant pseudo-differential operators on a Lie group. We give examples of bounded below pseudo-differential elliptic operators on \(\mathbb {R}^d\) by using the theory of Poisson process and the Garding inequality. In the two cases, there are no stochastic processes because the considered semi-groups do not preserve positivity.


Malliavin calculus Pseudo-differential operators Generalized Poisson processes Garding inequality 


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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Laboratoire de MathématiquesUniversité de Bourgogne-Franche-ComtéBesançonFrance

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