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Zap. Nauchn. Sem. POMI, 2018, Volume 474, Pages 183–194 (Mi znsl6677)  

This article is cited in 1 scientific paper (total in 1 paper)

Nonprobabilistic analogues of the Cauchy process

A. K. Nikolaeva, M. V. Platonovabc

a Saint Petersburg State University, Saint Petersburg, Russia
b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
c Chebyshev Laboratory, St. Petersburg State University, Department of Mathematics and Mechanics, St. Petersburg, Russia

Abstract: It is known that a solution of the Cauchy problem for an evolution equation having a convolution operator with a generalized function $|x|^{-2}$, in the right-hand side admits a probabilistic representation in the form of the expectation of a trajectory functional of the Cauchy process. We construct similar representations for evolution equations having a convolution operator with a generalized function $(-1)^m|x|^{-2m-2}$ for arbitrary $m\in\mathbf{N}$.

Key words and phrases: Random processes, Cauchy process, evolution equation, limit theorem.

Full text: PDF file (177 kB)
References: PDF file   HTML file
UDC: 519.2
MSC: 28C20, 60H05, 60G57
Received: 26.10.2018

Citation: A. K. Nikolaev, M. V. Platonova, “Nonprobabilistic analogues of the Cauchy process”, Probability and statistics. Part 27, Zap. Nauchn. Sem. POMI, 474, POMI, St. Petersburg, 2018, 183–194

Citation in format AMSBIB
\Bibitem{NikPla18}
\by A.~K.~Nikolaev, M.~V.~Platonova
\paper Nonprobabilistic analogues of the Cauchy process
\inbook Probability and statistics. Part~27
\serial Zap. Nauchn. Sem. POMI
\yr 2018
\vol 474
\pages 183--194
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6677}


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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. A. K. Nikolaev, M. V. Platonova, “Predelnye teoremy o skhodimosti k obobschennym protsessam tipa Koshi”, Veroyatnost i statistika. 28, Zap. nauchn. sem. POMI, 486, POMI, SPb., 2019, 214–228  mathnet
  • Записки научных семинаров ПОМИ
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