Deformation Quantization by Moyal Star-Product and Stratonovich Chaos
We make a deformation quantization by Moyal star-product on a space of functions endowed with the normalized Wick product and where Stratonovich chaos are well defined.
math.QA↗
arXiv subjects
Rémi Léandre
Publications and source records attributed to Rémi Léandre.
Varadhan estimates for a degenerated convolution semi-group: upper bound
We give a proof of Varadhan estimates for a degenerated jump process with independent increments with more and more jumps which become smaller and smaller. The proof uses the Malliavin Calculus of Bismut type for jump process in semi-group theory and Wentzel-Freidlin estimates for jump process in semi-group theory.
math.PR↗
Hochschild Cohomology Theories in White Noise Analysis
We show that the continuous Hochschild cohomology and the differential Hochschild cohomology of the Hida test algebra endowed with the normalized Wick product are the same.
math.QA↗
The geometry of Brownian surfaces
Motivated by Segal's axiom of conformal field theory, we do a survey on geometrical random fields. We do a history of continuous random fields in order to arrive at a field theoretical analog of Klauder's quantization in Hamiltonian quantum mechanic by using infinite dimensional Airault-Malliavin Brownian motion.
math.PR↗
Stochastic cohomology of the frame bundle of the loop space
We study the differential forms over the frame bundle of the based loop space. They are stochastics in the sense that we put over this frame bundle a probability measure. In order to understand the curvatures phenomena which appear when we look at the Lie bracket of two horizontal vector fields, we impose some regularity assumptions over the kernels of the differential forms. This allows us to define an exterior stochastic differential derivative over these forms.
math-ph↗