Differential and Integral Equations

Unique continuation for stochastic parabolic equations

Xu Zhang

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Abstract

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

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

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356039060

Mathematical Reviews number (MathSciNet)
MR2479663

Zentralblatt MATH identifier
1224.60163

Subjects
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

Citation

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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