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Feynman-Kac formula, λ-Poisson kernels and λ-Green functions of half-spaces and balls in hyperbolic spaces

Tomasz Byczkowski, Jacek Małecki, Tomasz Żak (2010)

Colloquium Mathematicae

We apply the Feynman-Kac formula to compute the λ-Poisson kernels and λ-Green functions for half-spaces or balls in hyperbolic spaces. We present known results in a unified way and also provide new formulas for the λ-Poisson kernels and λ-Green functions of half-spaces in ℍⁿ and for balls in real and complex hyperbolic spaces.

Fluctuations of brownian motion with drift.

Joseph G. Conlon, Peder Olsen (1999)

Publicacions Matemàtiques

Consider 3-dimensional Brownian motion started on the unit sphere {|x| = 1} with initial density ρ. Let ρt be the first hitting density on the sphere {|x| = t + 1}, t > 0. Then the linear operators Tt defined by Tt ρ = ρt form a semigroup with an infinitesimal generator which is approximately the square root of the Laplacian. This paper studies the analogous situation for Brownian motion with a drift b, where b is small in a suitable scale invariant norm.

Fredholm determinants

Henry McKean (2011)

Open Mathematics

The article provides with a down to earth exposition of the Fredholm theory with applications to Brownian motion and KdV equation.

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