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Ukrainian Mathematical Journal

, Volume 70, Issue 8, pp 1275–1287 | Cite as

On the Fundamental Solution of the Cauchy Problem for Kolmogorov Systems of the Second Order

  • H. P. Malyts’ka
  • I. V. Burtnyak
Article
  • 6 Downloads

We study the structure of the fundamental solution of the Cauchy problem for a class of systems of ultraparabolic equations with finitely many groups of variables degenerating parabolicity

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References

  1. 1.
    H. P. Malyts’ka, “Systems of equations of Kolmogorov type,” Ukr. Mat. Zh., 60, No. 12, 1650–1663 (2008); English translation : Ukr. Math. J., 60, No. 12, 1937–1954 (2008).Google Scholar
  2. 2.
    H. P. Malyts’ka, “Fundamental solution matrix of the Cauchy problem for a class of systems of Kolmogorov-type equations,” Different. Equat., 46, No. 5, 753–757 (2010).MathSciNetCrossRefGoogle Scholar
  3. 3.
    S. D. Eidelman, S. D. Ivasyshen, and A. N. Kochubei, Analytic Methods in the Theory of Differential and Pseudo-Differential Equations of Parabolic Type, Birkhäuser, Basel (2004).Google Scholar
  4. 4.
    S. D. Eidelman, S. D. Ivasyshen, and H. P. Malytska, “A modified Levi method: development and application,” Dop. Nats. Akad. Nauk Ukr., Ser. Mat., Prirodoznav., Tekh. Nauky, No. 5, 14–19 (1998).Google Scholar
  5. 5.
    S. Polidoro, “On a class of ultraparabolic operators of Kolmogorov–Fokker–Planck type,” Le Mathematiche, 49, 53–105 (1994).MathSciNetzbMATHGoogle Scholar
  6. 6.
    C. Cinti, A. Pascucci, and S. Polidoro, “Pointwise estimates for solutions to a class of non-homogeneous Kolmogorov equations,” Math. Ann., 340, No. 2, 237–264 (2008).MathSciNetCrossRefGoogle Scholar
  7. 7.
    S. D. Ivasyshen and H. P. Ivasyuk, “On the fundamental solutions of the Cauchy problem for the Fokker–Planck–Kolmogorov equations for some degenerate diffusion processes,” Mat. Komp. Model., 116–126 (2011).Google Scholar
  8. 8.
    I. V. Burtnyak and H. P. Malyts’ka, “A model of path-dependent volatility for the FSTS index,” Biznes Inform, No. 3, 48–50 (2012).Google Scholar
  9. 9.
    I. V. Burtnyak and H. P. Malyts’ka, “Evaluation of the option pricing by the methods of spectral analysis,” Biznes Inform, No. 4, 152–158 (2013).Google Scholar
  10. 10.
    R. Courant, Partial Differential Equations [Russian translation], Mir, Moscow (1964).Google Scholar
  11. 11.
    S. D. Éidel’man, Parabolic Systems [in Russian], Nauka, Moscow (1964).Google Scholar
  12. 12.
    I. V. Burtnyak and H. P. Malyts’ka, “Fundamental matrices of solutions of one class of degenerate parabolic systems,” Karpat. Mat. Publ., 4, No. 1, 12–22 (2012).Google Scholar
  13. 13.
    H. P. Malyts’ka, “On the structure of the fundamental solution of the Cauchy problem for the elliptic-parabolic equations generalizing the diffusion equation with inertia,” Visn. Nats. Univ. “L’vivs’ka Politekhnika,” Ser. Prykl. Mat., No. 411, 221–228 (2000).Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • H. P. Malyts’ka
    • 1
  • I. V. Burtnyak
    • 1
  1. 1.Stefanyk Precarpathian National UniversityIvano-Frankivs’kUkraine

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