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Convergence of some integrals associated with Bessel processes. (English. Russian original) Zbl 0982.60077
Theory Probab. Appl. 45, No. 2, 195-209 (2000); translation from Teor. Veroyatn. Primen. 45, No. 2, 251-267 (2000).
Let $$\rho_t, t\geq 0$$, be a $$\delta$$-dimensional Bessel process started at $$\rho_0\geq 0$$ and $$f$$ be a positive Borel function. The author studies the convergence of the Lebesgue integrals for the process $$f(\rho_t)$$. The obtained results are applied to prove that two Bessel processes of different dimensions have singular distributions.
##### MSC:
 60J60 Diffusion processes
##### Keywords:
Bessel process; Borel function; singularity of distribution
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