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Matematicheskie Zametki, 2007, Volume 82, Issue 3, Pages 401–410
DOI: https://doi.org/10.4213/mzm3849 (Mi mzm3849) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On Multiple Integrals of Special Form

R. N. Miroshin

Saint-Petersburg State University
Full-text PDF (397 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm3849
Abstract: Multiple integrals generalizing the iterated kernels of integral operators are expressed as single integrals in the case of a special representation of the kernel (this is our theorem). Besides integral equations, Markov processes involve these integrals as well. As a consequence of the theorem, we obtain transition probability densities of certain Markov processes. As an illustration, we consider nine examples.
Keywords: multiple integral, integral operator, iterated kernel, Markov process, Fourier integral transform, Hankel integral transform, Bessel function.
Received: 17.05.2006
Revised: 13.02.2007
English version:
Mathematical Notes, 2007, Volume 82, Issue 3, Pages 357–365
DOI: https://doi.org/10.1134/S000143460709009X
Bibliographic databases:
UDC: 518.2
Language: Russian
Citation: R. N. Miroshin, “On Multiple Integrals of Special Form”, Mat. Zametki, 82:3 (2007), 401–410; Math. Notes, 82:3 (2007), 357–365
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm3849
  • https://doi.org/10.4213/mzm3849
  • https://www.mathnet.ru/eng/mzm/v82/i3/p401
    • This publication is cited in the following 3 articles:
    1. R. N. Miroshin, “Special solutions of the Chapman–Kolmogorov equation for multidimensional-state Markov processes with continuous time”, Vestnik St.Petersb. Univ.Math., 49:2 (2016), 122  crossref
    2. R. N. Miroshin, “Representation of a Multiple Integral of Special Form by a Series”, Math. Notes, 93:1 (2013), 137–142  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. R. N. Miroshin, “On the solution of the Chapman-Kolmogorov integral equation in the form of a series”, Vestnik St.Petersb. Univ.Math., 42:2 (2009), 130  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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