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Pathwise uniqueness for stochastic heat equations with Hölder continuous coefficients: the white noise case
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  • Published: 11 September 2009

Pathwise uniqueness for stochastic heat equations with Hölder continuous coefficients: the white noise case

  • Leonid Mytnik1 &
  • Edwin Perkins2 

Probability Theory and Related Fields volume 149, pages 1–96 (2011)Cite this article

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  • 39 Citations

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Abstract

We prove pathwise uniqueness for solutions of parabolic stochastic pde’s with multiplicative white noise if the coefficient is Hölder continuous of index γ > 3/4. The method of proof is an infinite-dimensional version of the Yamada–Watanabe argument for ordinary stochastic differential equations.

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Author information

Authors and Affiliations

  1. Faculty of Industrial Engineering and Management, Technion, Israel Institute of Technology, 32000, Haifa, Israel

    Leonid Mytnik

  2. Department of Mathematics, The University of British Columbia, 1984 Mathematics Road, Vancouver, BC, V6T 1Z2, Canada

    Edwin Perkins

Authors
  1. Leonid Mytnik
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  2. Edwin Perkins
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Corresponding author

Correspondence to Edwin Perkins.

Additional information

L. Mytnik was supported in part by the Israel Science Foundation (grant No. 1162/06).

E. Perkins was supported by an NSERC Research grant.

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Cite this article

Mytnik, L., Perkins, E. Pathwise uniqueness for stochastic heat equations with Hölder continuous coefficients: the white noise case. Probab. Theory Relat. Fields 149, 1–96 (2011). https://doi.org/10.1007/s00440-009-0241-7

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  • Received: 29 August 2008

  • Revised: 26 June 2009

  • Published: 11 September 2009

  • Issue Date: February 2011

  • DOI: https://doi.org/10.1007/s00440-009-0241-7

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Keywords

  • Stochastic partial differential equations
  • Pathwise uniqueness
  • White noise

Mathematics Subject Classification (2000)

  • Primary 60H15
  • Secondary 60G60
  • 60H10
  • 60H40
  • 60K35
  • 60J80
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