Geodesic
Convergence of some integrals associated with Bessel processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 45 (2000) no. 2, pp. 251-267

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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. 
@article{TVP_2000_45_2_a2,
     author = {A. S. Cherny},
     title = {Convergence of some integrals associated with {Bessel} processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {251--267},
     publisher = {mathdoc},
     volume = {45},
     number = {2},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2000_45_2_a2/}
}
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A. S. Cherny. Convergence of some integrals associated with Bessel processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 45 (2000) no. 2, pp. 251-267. http://geodesic.mathdoc.fr/item/TVP_2000_45_2_a2/