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Teor. Veroyatnost. i Primenen., 2000, Volume 45, Issue 2, Pages 251–267 (Mi tvp462)  

This article is cited in 10 scientific papers (total in 10 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.

DOI: https://doi.org/10.4213/tvp462

Full text: PDF file (766 kB)

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

Bibliographic databases:

Received: 21.11.1998

Citation: A. S. Cherny, “Convergence of some integrals associated with Bessel processes”, Teor. Veroyatnost. i Primenen., 45:2 (2000), 251–267; Theory Probab. Appl., 45:2 (2001), 195–209

Citation in format AMSBIB
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\by A.~S.~Cherny
\paper Convergence of some integrals associated with Bessel processes
\jour Teor. Veroyatnost. i Primenen.
\yr 2000
\vol 45
\issue 2
\pages 251--267
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1967756}
\zmath{https://zbmath.org/?q=an:0982.60077}
\transl
\jour Theory Probab. Appl.
\yr 2001
\vol 45
\issue 2
\pages 195--209
\crossref{https://doi.org/10.1137/S0040585X97978178}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000169004700002}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. A. Urusov, A. S. Cherny, “Separating times for measures on filtered spaces”, Theory Probab. Appl., 48:2 (2004), 337–347  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Cherny A.S., Engelbert H.-J., “Singular stochastic differential equations”, Singular Stochastic Differential Equations, Lecture Notes in Mathematics, 1858, 2005, 1  crossref  mathscinet  zmath  isi
    3. Salminen P., Yor M., “Properties of perpetual integral functionals of Brownian motion with drift”, Annales de l Institut Henri Poincare–Probabilites et Statistiques, 41:3 (2005), 335–347  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Cherny A., Urusov M., “On the absolute continuity and singularity of measures on filtered spaces: Separating times”, From Stochastic Calculus to Mathematical Finance: The Shiryaev Festschrift, 2006, 125–168  crossref  mathscinet  zmath  isi
    5. Vostrikova L., “On Regularity Properties of Bessel Flow”, Stochastics, 81:5 (2009), 431–453  crossref  mathscinet  zmath  isi
    6. Matsumoto A., Yano K., “On a Zero-One Law for the Norm Process of Transient Random Walk”, Seminaire de Probabilites XLIII, Lecture Notes in Mathematics, 2006, 2011, 105–126  crossref  mathscinet  zmath  isi  scopus
    7. Mijatovic A., Urusov M., “Convergence of Integral Functionals of One-Dimensional Diffusions”, Electron. Commun. Probab., 17 (2012), 1–13  crossref  mathscinet  isi  scopus
    8. Blei S., “On Symmetric and Skew Bessel Processes”, Stoch. Process. Their Appl., 122:9 (2012), 3262–3287  crossref  mathscinet  zmath  isi  scopus
    9. Mijatovic A., Mramor V., Uribe Bravo G., “Projections of Spherical Brownian Motion”, Electron. Commun. Probab., 23 (2018)  crossref  isi  scopus
    10. Georgiou N., Mijatovic A., Wade A.R., “Invariance Principle For Non-Homogeneous Random Walks”, Electron. J. Probab., 24 (2019), 48  crossref  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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