Hitting half-spaces or spheres by Ornstein-Uhlenbeck type diffusions

Tomasz Byczkowski; Jakub Chorowski; Piotr Graczyk; Jacek Małecki

The search session has expired. Please query the service again.

Displaying similar documents to “Hitting half-spaces or spheres by Ornstein-Uhlenbeck type diffusions”

Poisson kernel and Green function of balls for complex hyperbolic Brownian motion

Tomasz Żak (2007)

Studia Mathematica

Similarity:

The aim of this paper is to give a description of the Poisson kernel and the Green function of balls in the complex hyperbolic space. The description is in terms of the hypergeometric function and unitary spherical harmonics in ℂⁿ.

Limiting behaviors of the Brownian motions on hyperbolic spaces

H. Matsumoto (2010)

Colloquium Mathematicae

Similarity:

Using explicit representations of the Brownian motions on hyperbolic spaces, we show that their almost sure convergence and the central limit theorems for the radial components as time tends to infinity can be easily obtained. We also give a straightforward strategy to obtain explicit expressions for the limit distributions or Poisson kernels.

Sharp estimates of the Green function of hyperbolic Brownian motion

Kamil Bogus, Tomasz Byczkowski, Jacek Małecki (2015)

Studia Mathematica

Similarity:

The main objective of the work is to provide sharp two-sided estimates of the λ-Green function, λ ≥ 0, of the hyperbolic Brownian motion of a half-space. We rely on the recent results obtained by K. Bogus and J. Małecki (2015), regarding precise estimates of the Bessel heat kernel for half-lines. We also substantially use the results of H. Matsumoto and M. Yor (2005) on distributions of exponential functionals of Brownian motion.

Hitting distributions of geometric Brownian motion

T. Byczkowski, M. Ryznar (2006)

Studia Mathematica

Similarity:

Let τ be the first hitting time of the point 1 by the geometric Brownian motion X(t) = x exp(B(t) - 2μt) with drift μ ≥ 0 starting from x > 1. Here B(t) is the Brownian motion starting from 0 with EB²(t) = 2t. We provide an integral formula for the density function of the stopped exponential functional $A (τ) = \int_{0}^{τ} X ² (t) d t$ and determine its asymptotic behaviour at infinity. Although we basically rely on methods developed in [BGS], the present paper covers the case of arbitrary drifts μ ≥ 0 and provides...

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

Similarity:

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.

Coalescence of skew brownian motions

Martin T. Barlow, Krzysztof Burdzy, Haya Kaspi, Avi Mandelbaum (2001)

Séminaire de probabilités de Strasbourg

Similarity:

Distributions of functionals of diffusions with jumps.

Borodin, A.N. (2005)

Zapiski Nauchnykh Seminarov POMI

Similarity:

The noise made by a Poisson snake.

Warren, Jon (2002)

Electronic Journal of Probability [electronic only]

Similarity:

Linear transformations of two independent Brownian motions and orthogonal decompositions of Brownian filtrations.

Ching-Tang Wu, Marc Yor (2002)

Publicacions Matemàtiques

Similarity:

Brownian motions defined as linear transformations of two independent Brownian motions are studied, together with certain orthogonal decompositions of Brownian filtrations.

Book review: Handbook of Brownian Motion - Facts and Formulae. Second Edition by A.N. Borodin, P. Salminen

Piotr Nowak (2003)

Control and Cybernetics

Similarity:

Wiener's test for the Brownian motion on the Heisenberg group

Jacek Cygan (1978)

Colloquium Mathematicae

Similarity:

On the analogy between self-gravitating Brownian particles and bacterial populations

Pierre-Henri Chavanis, Magali Ribot, Carole Rosier, Clément Sire (2004)

Banach Center Publications

Similarity:

We develop the analogy between self-gravitating Brownian particles and bacterial populations. In the high friction limit, the self-gravitating Brownian gas is described by the Smoluchowski-Poisson system. These equations can develop a self-similar collapse leading to a finite time singularity. Coincidentally, the Smoluchowski-Poisson system corresponds to a simplified version of the Keller-Segel model of bacterial populations. In this biological context, it describes the chemotactic...

A trivariate law for certain processes related to perturbed brownian motions

Philippe Carmona, Frédérique Petit, Marc Yor (2004)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

On the constructions of the skew Brownian motion.

Lejay, Antoine (2006)

Probability Surveys [electronic only]

Similarity:

On the joining of sticky brownian motion

Jonathan Warren (1999)

Séminaire de probabilités de Strasbourg

Similarity: