Differential and Integral Equations

Unique continuation for stochastic parabolic equations

Xu Zhang

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This paper is devoted to a study of the unique continuation property for stochastic parabolic equations. Due to the adapted nature of solutions in the stochastic situation, classical approaches to treat the unique continuation problem for deterministic equations do not work. Our method is based on a suitable partial Holmgren coordinate transform and a stochastic version of Carleman estimate.

Article information

Differential Integral Equations, Volume 21, Number 1-2 (2008), 81-93.

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 35B60: Continuation and prolongation of solutions [See also 58A15, 58A17, 58Hxx] 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 93B05: Controllability 93E03: Stochastic systems, general


Zhang, Xu. Unique continuation for stochastic parabolic equations. Differential Integral Equations 21 (2008), no. 1-2, 81--93. https://projecteuclid.org/euclid.die/1356039060

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