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Teor. Veroyatnost. i Primenen., 2016, Volume 61, Issue 3, Pages 417–438 (Mi tvp5067)  

This article is cited in 4 scientific papers (total in 4 papers)

Probabilistic representation for Cauchy problem solution for evolution equation with Riemann–Liouville operator

M. V. Platonova

Chebyshev Laboratory, St. Petersburg State University, Department of Mathematics and Mechanics

Abstract: This paper studies properties of probabilistic approximation of a solution of the Cauchy problem for evolution equations with fractional differential operators of order more than two. To this end we construct analogous one-sided $\alpha$-stable distributions for noninteger $\alpha>2$. Although densities of these distributions are signed functions, using generalized functions methods, it is possible to give them an exact probability sense.

Keywords: Liouville–Riemann operator, evolution equation, stable distribution.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00443_a


DOI: https://doi.org/10.4213/tvp5067

Full text: PDF file (354 kB)
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English version:
Theory of Probability and its Applications, 2017, 61:3, 389–407

Bibliographic databases:

Received: 07.03.2016

Citation: M. V. Platonova, “Probabilistic representation for Cauchy problem solution for evolution equation with Riemann–Liouville operator”, Teor. Veroyatnost. i Primenen., 61:3 (2016), 417–438; Theory Probab. Appl., 61:3 (2017), 389–407

Citation in format AMSBIB
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\paper Probabilistic representation for Cauchy problem solution for evolution equation with Riemann--Liouville operator
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. V. Platonova, “A probabilistic representation of the Cauchy problem solution for an evolution equation with the differential operator of the order greater than 2”, J. Math. Sci. (N. Y.), 229:6 (2018), 744–755  mathnet  crossref  mathscinet
    2. I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “Probabilistic Approximation of the Evolution Operator”, Funct. Anal. Appl., 52:2 (2018), 101–112  mathnet  crossref  crossref  mathscinet  isi  elib
    3. Yu. Kozachenko, E. Orsingher, L. Sakhno, O. Vasylyk, “Estimates for functionals of solutions to higher-order heat-type equations with random initial conditions”, J. Stat. Phys., 172:6 (2018), 1641–1662  crossref  mathscinet  zmath  isi  scopus
    4. A. K. Nikolaev, M. V. Platonova, “Neveroyatnostnye analogi protsessa Koshi”, Veroyatnost i statistika. 27, Zap. nauchn. sem. POMI, 474, POMI, SPb., 2018, 183–194  mathnet
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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