T. Byczkowski

collaborators

2 papers

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…