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Teor. Veroyatnost. i Primenen., 2002, Volume 47, Issue 1, Pages 152–159 (Mi tvp3376)  

This article is cited in 6 scientific papers (total in 6 papers)

Short Communications

Hölder estimates for solutions of parabolic SPDEs

S. B. Kuksina, N. S. Nadirashvilib, A. L. Piatnitskicd

a Heriot Watt University
b University of Chicago
c P. N. Lebedev Physical Institute, Russian Academy of Sciences
d Narvik Institute of Technology

Abstract: This paper considers second-order stochastic partial differential equations with additive noise given in a bounded domain of $R^n$. We suppose that the coefficients of the noise are $L^p$-functions with sufficiently large $p$. We prove that the solutions are Hölder-continuous functions almost surely (a.s.) and that the respective Hölder norms have finite momenta of any order.

Keywords: stochastic equation, Hölder-continuous function.

DOI: https://doi.org/10.4213/tvp3376

Full text: PDF file (805 kB)

English version:
Theory of Probability and its Applications, 2003, 47:1, 157–163

Bibliographic databases:

Received: 28.08.2000

Citation: S. B. Kuksin, N. S. Nadirashvili, A. L. Piatnitski, “Hölder estimates for solutions of parabolic SPDEs”, Teor. Veroyatnost. i Primenen., 47:1 (2002), 152–159; Theory Probab. Appl., 47:1 (2003), 157–163

Citation in format AMSBIB
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\by S.~B.~Kuksin, N.~S.~Nadirashvili, A.~L.~Piatnitski
\paper H\"older estimates for solutions of parabolic SPDEs
\jour Teor. Veroyatnost. i Primenen.
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\issue 1
\pages 152--159
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\transl
\jour Theory Probab. Appl.
\yr 2003
\vol 47
\issue 1
\pages 157--163
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kim Kyeong-Hun, “$L_q(L_p)$ theory and Hölder estimates for parabolic SPDEs”, Stochastic Process. Appl., 114:2 (2004), 313–330  crossref  mathscinet  zmath  isi  scopus
    2. Kim Kyeong-Hun, “On $L_p$-theory of stochastic partial differential equations of divergence form in $C^1$ domains”, Probab. Theory Related Fields, 130:4 (2004), 473–492  crossref  mathscinet  zmath  isi  scopus
    3. Liu Sh. Zhang Y., “Stability of Stochastic 2-D Systems”, Appl. Math. Comput., 219:1 (2012), 197–212  crossref  mathscinet  zmath  isi  elib  scopus
    4. Dareiotis K., Gerencser M., “Local L-estimates, weak Harnack inequality, and stochastic continuity of solutions of SPDEs”, J. Differ. Equ., 262:1 (2017), 615–632  crossref  mathscinet  zmath  isi  elib  scopus
    5. Wei J., Duan J., Lv G., “Schauder Estimates For Stochastic Transport-Diffusion Equations With Levy Processes”, J. Math. Anal. Appl., 474:1 (2019), 1–22  crossref  mathscinet  zmath  isi  scopus
    6. Tian R., Ding L., Wei J., Zheng S., “Holder Estimates of Mild Solutions For Nonlocal Spdes”, Adv. Differ. Equ., 2019, 159  crossref  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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