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Teoriya Veroyatnostei i ee Primeneniya, 1969, Volume 14, Issue 1, Pages 127–130 (Mi tvp1123)  

This article is cited in 57 scientific papers (total in 57 papers)

Short Communications

Symmetric stable processes as traces of degenerate diffusion processes

S. A. Molchanov, E. Ostrovskii

Moscow
Abstract: In this article we show that symmetric stable processes may be considered as traces of diffusion processes of a special type (Bessel processes). This result generalizes the well-known theorem due to Spitzer concerning a similar representation of Cauchy processes.
Received: 27.02.1968
English version:
Theory of Probability and its Applications, 1969, Volume 14, Issue 1, Pages 128–131
DOI: https://doi.org/10.1137/1114012
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. A. Molchanov, E. Ostrovskii, “Symmetric stable processes as traces of degenerate diffusion processes”, Teor. Veroyatnost. i Primenen., 14:1 (1969), 127–130; Theory Probab. Appl., 14:1 (1969), 128–131
Citation in format AMSBIB
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\by S.~A.~Molchanov, E.~Ostrovskii
\paper Symmetric stable processes as traces of degenerate diffusion processes
\jour Teor. Veroyatnost. i Primenen.
\yr 1969
\vol 14
\issue 1
\pages 127--130
\mathnet{http://mi.mathnet.ru/tvp1123}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=247668}
\zmath{https://zbmath.org/?q=an:0281.60091|0238.60060}
\transl
\jour Theory Probab. Appl.
\yr 1969
\vol 14
\issue 1
\pages 128--131
\crossref{https://doi.org/10.1137/1114012}
Linking options:
  • https://www.mathnet.ru/eng/tvp1123
  • https://www.mathnet.ru/eng/tvp/v14/i1/p127
  • This publication is cited in the following 57 articles:
    1. Xavier Fernández-Real, Xavier Ros-Oton, Progress in Mathematics, 350, Integro-Differential Elliptic Equations, 2024, 1  crossref
    2. Susanna Terracini, Giorgio Tortone, Stefano Vita, “Higher Order Boundary Harnack Principle via Degenerate Equations”, Arch Rational Mech Anal, 248:2 (2024)  crossref
    3. Zhen-Qing Chen, Lidan Wang, “Inverse local time of one-dimensional diffusions and its comparison theorem”, Sci. China Math., 2024  crossref
    4. Fedor Bakharev, Sergey Matveenko, “Fractional Laplacian in V‐shaped waveguide”, Mathematische Nachrichten, 2024  crossref
    5. A. I. Nazarov, A. P. Shcheglova, “Solutions with various structures for semilinear equations in Rn driven by fractional Laplacian”, Calc. Var., 62:4 (2023)  crossref
    6. Xinyu Cheng, Dong Li, Wen Yang, “On the equivalence of classical Helmholtz equation and fractional Helmholtz equation with arbitrary order”, Commun. Contemp. Math., 25:09 (2023)  crossref
    7. Konstantinos Tzirakis, Fixed Point Theory and Chaos, 2023  crossref
    8. Mateusz Kwaśnicki, “Boundary traces of shift-invariant diffusions in half-plane”, Ann. Inst. H. Poincaré Probab. Statist., 59:1 (2023)  crossref
    9. Luca Fanelli, Luz Roncal, “Kato–Ponce estimates for fractional sublaplacians in the Heisenberg group”, Bulletin of London Math Soc, 55:2 (2023), 611  crossref
    10. Mateusz Kwaśnicki, “Harmonic extension technique for non-symmetric operators with completely monotone kernels”, Calc. Var., 61:6 (2022)  crossref
    11. Marvin Fritz, Ustim Khristenko, Barbara Wohlmuth, “Equivalence between a time-fractional and an integer-order gradient flow: The memory effect reflected in the energy”, Advances in Nonlinear Analysis, 12:1 (2022)  crossref
    12. Soojung Kim, Youngae Lee, “Finite Morse Index Solutions of the Fractional Henon–Lane–Emden Equation with Hardy Potential”, Taiwanese J. Math., 26:2 (2022)  crossref
    13. Alexander I. Nazarov, “On comparison of fractional Laplacians”, Nonlinear Analysis, 218 (2022), 112790  crossref
    14. Vincent Millot, Marc Pegon, Armin Schikorra, “Partial Regularity for Fractional Harmonic Maps into Spheres”, Arch Rational Mech Anal, 242:2 (2021), 747  crossref
    15. Sigurd Assing, John Herman, “Extension technique for functions of diffusion operators: a stochastic approach”, Electron. J. Probab., 26:none (2021)  crossref
    16. Jacek Jakubowski, Maciej Wiśniewolski, “A convolution formula for the local time of an Itô diffusion reflecting at 0 and a generalized Stroock–Williams equation”, Bernoulli, 27:3 (2021)  crossref
    17. Christian Glusa, Harbir Antil, Marta D'Elia, Bart van Bloemen Waanders, Chester J. Weiss, “A Fast Solver for the Fractional Helmholtz Equation”, SIAM J. Sci. Comput., 43:2 (2021), A1362  crossref
    18. Jan Meichsner, Christian Seifert, “On the Harmonic Extension Approach to Fractional Powers in Banach Spaces”, Fract Calc Appl Anal, 23:4 (2020), 1054  crossref
    19. Anna Lischke, Guofei Pang, Mamikon Gulian, Fangying Song, Christian Glusa, Xiaoning Zheng, Zhiping Mao, Wei Cai, Mark M. Meerschaert, Mark Ainsworth, George Em Karniadakis, “What is the fractional Laplacian? A comparative review with new results”, Journal of Computational Physics, 404 (2020), 109009  crossref
    20. Vincent Millot, Yannick Sire, Kelei Wang, “Asymptotics for the Fractional Allen–Cahn Equation and Stationary Nonlocal Minimal Surfaces”, Arch Rational Mech Anal, 231:2 (2019), 1129  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    Теория вероятностей и ее применения Theory of Probability and its Applications
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