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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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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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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DOI: https://doi.org/10.1007/s00440-009-0241-7
Keywords
- Stochastic partial differential equations
- Pathwise uniqueness
- White noise
Mathematics Subject Classification (2000)
- Primary 60H15
- Secondary 60G60
- 60H10
- 60H40
- 60K35
- 60J80