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Izv. Akad. Nauk SSSR Ser. Mat., 1988, Volume 52, Issue 5, Pages 909–934 (Mi izv1211)  

This article is cited in 7 scientific papers (total in 7 papers)

Parabolic pseudodifferential equations, hypersingular integrals, and Markov processes

A. N. Kochubei


Abstract: A fundamental solution of the Cauchy problem is constructed and investigated for the equation $\frac{\partial u}{\partial t}+Au=f$, where $A$ is a pseudodifferential operator whose symbol is a sum of homogeneous functions. The results are used for an analytic construction of discontinuous Markov processes.
Bibliography: 42 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1989, 33:2, 233–259

Bibliographic databases:

UDC: 517.43+519.21
MSC: Primary 35S10, 60J25; Secondary 42B20, 35K30
Received: 10.04.1986

Citation: A. N. Kochubei, “Parabolic pseudodifferential equations, hypersingular integrals, and Markov processes”, Izv. Akad. Nauk SSSR Ser. Mat., 52:5 (1988), 909–934; Math. USSR-Izv., 33:2 (1989), 233–259

Citation in format AMSBIB
\Bibitem{Koc88}
\by A.~N.~Kochubei
\paper Parabolic pseudodifferential equations, hypersingular integrals, and Markov processes
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1988
\vol 52
\issue 5
\pages 909--934
\mathnet{http://mi.mathnet.ru/izv1211}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=972089}
\zmath{https://zbmath.org/?q=an:0682.35113}
\transl
\jour Math. USSR-Izv.
\yr 1989
\vol 33
\issue 2
\pages 233--259
\crossref{https://doi.org/10.1070/IM1989v033n02ABEH000825}


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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. A. N. Kochubei, “Parabolic equations over the field of $p$-adic numbers”, Math. USSR-Izv., 39:3 (1992), 1263–1280  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. V. A. Litovchenko, “The Cauchy problem for one class of parabolic pseudodifferential systems with nonsmooth symbols”, Siberian Math. J., 49:2 (2008), 300–316  mathnet  crossref  mathscinet  zmath  isi
    3. BJÖRN BÖTTCHER, RENÉ L. SCHILLING, “APPROXIMATION OF FELLER PROCESSES BY Markov CHAINS WITH Lévy INCREMENTS”, Stoch. Dyn, 09:01 (2009), 71  crossref
    4. Vassili N. Kolokoltsov, “The Lévy–Khintchine type operators with variable Lipschitz continuous coefficients generate linear or nonlinear Markov processes and semigroups”, Probab Theory Relat Fields, 2010  crossref
    5. Mirjana Stojanović, “Numerical method for solving diffusion-wave phenomena”, Journal of Computational and Applied Mathematics, 235:10 (2011), 3121  crossref
    6. Zhen-Qing Chen, Xicheng Zhang, “Heat kernels and analyticity of non-symmetric jump diffusion semigroups”, Probab. Theory Relat. Fields, 2015  crossref
    7. M. M. Osypchuk, “On some perturbations of a symmetric stable process and the corresponding Cauchy problems”, Theory Stoch. Process., 21(37):1 (2016), 64–72  mathnet  mathscinet
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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