This article is cited in 11 papers

Convergence of some integrals associated with Bessel processes

A. S. Cherny

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We study the convergence of the Lebesgue integrals for the processes $f(\rho_t)$. Here, $(\rho_t,\,t\ge0)$ is the $\delta$-dimensional Bessel process started at $\rho_0\ge0$ and $f$ is a positive Borel function. The obtained results are applied to prove that two Bessel processes of different dimensions have singular distributions.

Keywords: Bessel processes, Engelbert–Schmidt zero–one law, Brownian local time, regular continuous strong Markov processes, singularity of distributions.

Received: 21.11.1998

DOI: 10.4213/tvp462

 English version: Theory of Probability and its Applications, 2001, 45:2, 195–209

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