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Teoriya Veroyatnostei i ee Primeneniya, 1998, Volume 43, Issue 2, Pages 331–348
DOI: https://doi.org/10.4213/tvp1468 (Mi tvp1468) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Strong Markov local Dirichlet processes and stochastic differential equations

H.-J. Engelbert, J. Wolf

Friedrich-Schiller-Universität, Fakultät für Mathematik und Informatik, Institut für Stochastik
Full-text PDF (897 kB) Citations (11)
DOI: https://doi.org/10.4213/tvp1468
Abstract: This paper states the necessary and sufficient conditions on the natural scale and the measure of convergence of the continuous strong Markov local Dirichlet process in order that the process has a representation in the form of a solution of some stochastic differential equation. The results are applied to the case of the Bessel process of arbitrary dimension.
Keywords: Bessel process, Dirichlet process, stochastic differential equations, local time, strong Markov processes.
English version:
Theory of Probability and its Applications, 1999, Volume 43, Issue 2, Pages 189–202
DOI: https://doi.org/10.1137/S0040585X97976829
Bibliographic databases:
Language: English
Citation: H.-J. Engelbert, J. Wolf, “Strong Markov local Dirichlet processes and stochastic differential equations”, Teor. Veroyatnost. i Primenen., 43:2 (1998), 331–348; Theory Probab. Appl., 43:2 (1999), 189–202
Citation in format AMSBIB
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\by H.-J.~Engelbert, J.~Wolf
\paper Strong Markov local Dirichlet processes and stochastic differential equations
\jour Teor. Veroyatnost. i Primenen.
\yr 1998
\vol 43
\issue 2
\pages 331--348
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\crossref{https://doi.org/10.4213/tvp1468}
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\zmath{https://zbmath.org/?q=an:0953.60043}
\transl
\jour Theory Probab. Appl.
\yr 1999
\vol 43
\issue 2
\pages 189--202
\crossref{https://doi.org/10.1137/S0040585X97976829}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000083189300002}
Linking options:
  • https://www.mathnet.ru/eng/tvp1468
  • https://doi.org/10.4213/tvp1468
  • https://www.mathnet.ru/eng/tvp/v43/i2/p331
    • This publication is cited in the following 11 articles:
    1. Alberto Ohashi, Francesco Russo, Alan Teixeira, “On SDEs for Bessel Processes in low dimension and path-dependent extensions”, ALEA, 20:2 (2023), 1111  crossref
    2. Alberto Ohashi, Francesco Russo, Alan Teixeira, “On path-dependent SDEs involving distributional drifts”, Modern Stochastics: Theory and Applications, 2022, 65  crossref
    3. Francesco Russo, Pierre Vallois, Bocconi & Springer Series, 11, Stochastic Calculus via Regularizations, 2022, 491  crossref
    4. Issoglio E., Russo F., “A Feynman-Kac Result Via Markov Bsdes With Generalised Drivers”, Bernoulli, 26:1 (2020), 728–766  crossref  isi
    5. Flandoli F., Issoglio E., Russo F., “Multidimensional stochastic differential equations with distributional drift”, Trans. Am. Math. Soc., 369:3 (2017), 1665–1688  crossref  mathscinet  zmath  isi  scopus
    6. Karatzas I. Ruf J., “Pathwise solvability of stochastic integral equations with generalized drift and non-smooth dispersion functions”, Ann. Inst. Henri Poincare-Probab. Stat., 52:2 (2016), 915–938  crossref  mathscinet  zmath  isi  scopus
    7. Russo F., Trutnau G., “Some parabolic PDEs whose drift is an irregular random noise in space”, Annals of Probability, 35:6 (2007), 2213–2262  crossref  mathscinet  zmath  isi  scopus
    8. Franco Flandoli, Francesco Russo, Jochen Wolf, “Some SDEs with distributional drift.”, Random Operators and Stochastic Equations, 12:2 (2004)  crossref
    9. Beghdadi-Sakrani S., “On pathwise uniqueness of stochastic differential equations without drift”, Journal of Theoretical Probability, 16:4 (2003), 789–812  crossref  mathscinet  zmath  isi  scopus
    10. Flandoli F., Russo F., Wolf J., “Some SDEs with distributional drift part I: General calculus”, Osaka Journal of Mathematics, 40:2 (2003), 493–542  mathscinet  zmath  isi
    11. Russo F., Vallois P., Wolf J., “A generalized class of Lyons–Zheng processes”, Bernoulli, 7:2 (2001), 363–379  crossref  mathscinet  zmath  isi  scopus
    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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