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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2006, Number 2, Pages 62–68 (Mi basm97)  

This article is cited in 3 scientific papers (total in 3 papers)

Discontinuous term of the distribution for Markovian random evolution in $\mathrm R^3$

Alexander D. Kolesnik

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Kishinev, Moldova

Abstract: We consider the random motion at constant finite speed in the space $R^3$ subject to the control of a homogeneous Poisson process and with uniform choice of directions on the unit 3-sphere. We obtain the explicit forms of the conditional characteristic function and conditional distribution when one change of direction occurs. We show that this conditional distribution represents a discontinuous term of the transition function of the motion.

Keywords and phrases: Random motions, finite speed, random evolution, characteristic functions, conditional distributions.

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Bibliographic databases:

MSC: Primary 60K99; Secondary 62G30; 60K35; 60J60; 60H30
Received: 30.05.2006
Language: English

Citation: Alexander D. Kolesnik, “Discontinuous term of the distribution for Markovian random evolution in $\mathrm R^3$”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2006, no. 2, 62–68

Citation in format AMSBIB
\Bibitem{Kol06}
\by Alexander~D.~Kolesnik
\paper Discontinuous term of the distribution for Markovian random evolution in~$\mathrm R^3$
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2006
\issue 2
\pages 62--68
\mathnet{http://mi.mathnet.ru/basm97}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2279089}
\zmath{https://zbmath.org/?q=an:1119.60084}


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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. Ukrainian Math. J., 60:12 (2008), 1915–1926  crossref  mathscinet  zmath  isi  elib  scopus
    2. Kolesnik A.D., “Random motions at finite speed in higher dimensions”, J. Stat. Phys., 131:6 (2008), 1039–1065  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Kolesnik A.D., “Asymptotic Relation For the Transition Density of the Three-Dimensional Markov Random Flight on Small Time Intervals”, J. Stat. Phys., 166:2 (2017), 434–452  crossref  mathscinet  zmath  isi  scopus
  • Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
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