867 research outputs found
Standardizing densities on Gaussian spaces
In the present note we investigate the problem of standardizing random
variables taking values on infinite dimensional Gaussian spaces. In particular,
we focus on the transformations induced on densities by the selected
standardization procedure. We discover that, under certain conditions, the Wick
exponentials are the key ingredients for treating this kind of problems.Comment: 12 page
Nash estimates and upper bounds for non-homogeneous Kolmogorov equations
We prove a Gaussian upper bound for the fundamental solutions of a class of
ultra-parabolic equations in divergence form. The bound is independent on the
smoothness of the coefficients and generalizes some classical results by Nash,
Aronson and Davies. The class considered has relevant applications in the
theory of stochastic processes, in physics and in mathematical finance.Comment: 21 page
-Liouville Theorems for Invariant Partial Differential Operators in
We prove some -Liouville theorems for hypoelliptic second order Partial
Differential Operators left translation invariant with respect to a Lie group
composition law in . Results for both solutions and subsolutions
are given
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