Kamil Bogus

activity

20152018

collaborators

3 papers

math.PR2018

Self-similar solutions of kinetic-type equations: the boundary case

Kamil Bogus, Dariusz Buraczewski, Alexander Marynych

For a time dependent family of probability measures $(ρ_{t})_{t \geq 0}$ we consider a kinetic-type evolution equation $\partial ϕ_{t} / \partial t + ϕ_{t} = Q ϕ_{t}$ where $\widehat…

math.AP2017

Asymptotic behaviour of the Bessel heat kernels

Kamil Bogus

We consider Dirichlet heat kernel $p_{a}^{(μ)} (t, x, y)$ for the Bessel differential operator $L^{(μ)} = \frac{d ^{2}}{d x ^{2}} + \frac{2 μ + 1}{2 x}$ , $μ \in R$ , in half-line $(a, \infty)$ , $…

math.PR2015

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 $λ$ -Green function of hyperbolic Brownian motion of a half-space. We strongly rely on recent results obtai…