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Density behaviour related to Lévy processes
Loïc Chaumont, Jacek Małecki
Let , and be the densities at time of a real Lévy process, its running supremum and the entrance law of the reflected excursions at the infimum. We…
Hitting distributions of planar Brownian motion
T. Byczkowski, J. Malecki, M. Ryznar
The purpose of the paper is to find the joint distribution of the hitting time and place of two-dimensional Brownian motion hitting the negative horizontal axis. We provide various…
The entrance law of the excursion measure of the reflected process for some classes of Lévy processes
Loïc Chaumont, Jacek Małecki
We provide integral formulae for the Laplace transform of the entrance law of the reflected excursions for symmetric Lévy processes in terms of their characteristic exponent. For s…
Universality classes for general random matrix flows
Jacek Małecki, José Luis Pérez
We consider matrix-valued processes described as solutions to stochastic differential equations of very general form. We study the family of the empirical measure-valued processes…
On squared Bessel particle systems
Piotr Graczyk, Jacek Malecki
We study the existence and uniqueness of SDEs describing squared Bessel particles systems in full generality. We define non-negative and non-colliding squared Bessel particle syste…
Sharp estimates of Green function of hyperbolic Brownian Motion
Kamil Bogus, Tomasz Byczkowski, Jacek Malecki
The main objective of the work is to provide sharp two-sided estimates of -Green function of hyperbolic Brownian motion of a half-space. We strongly rely on recent results obtai…