T. Byczkowski

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math.PR2006

Bessel Potentials, Hitting Distributions and Green Functions

T. Byczkowski, M. Ryznar, J. Malecki

The purpose of this paper is to find explicit formulas for basic objects pertaining the local potential theory of the operator $(I - Δ)^{α /2}$ , $0 < α < 2$ . The potential theory of this…

math.PR2005

Poisson kernels of half-spaces in real hyperbolic spaces

T. Byczkowski, P. Graczyk, A. Stos

We provide an integral formula for the Poisson kernel of half-spaces for Brownian motion in real hyperbolic space $\H^n$. This enables us to find asymptotic properties of the kerne…

math.PR2005

Hitting distributions of geometric Brownian motion

T. Byczkowski, M. Ryznar

Let $τ$ be the first hitting time of the point 1 by the geometric Brownian motion $X (t) = x exp (B (t) - 2 μ t)$ with drift $μ \geq 0$ starting from $x > 1$ . Here $B (t)$ is the Brownian mot…