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Law of large numbers and central limit theorem for randomly forced PDE's
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  • Published: 03 May 2005

Law of large numbers and central limit theorem for randomly forced PDE's

  • Armen Shirikyan1 

Probability Theory and Related Fields volume 134, pages 215–247 (2006)Cite this article

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Abstract

We consider a class of dissipative PDE's perturbed by an external random force. Under the condition that the distribution of perturbation is sufficiently non-degenerate, a strong law of large numbers (SLLN) and a central limit theorem (CLT) for solutions are established and the corresponding rates of convergence are estimated. It is also shown that the estimates obtained are close to being optimal. The proofs are based on the property of exponential mixing for the problem in question and some abstract SLLN and CLT for mixing-type Markov processes.

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Authors and Affiliations

  1. Laboratoire de Mathématiques, Université de Paris-Sud XI, Bâtiment 425, 91405, Orsay Cedex, France

    Armen Shirikyan

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  1. Armen Shirikyan
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Correspondence to Armen Shirikyan.

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Shirikyan, A. Law of large numbers and central limit theorem for randomly forced PDE's. Probab. Theory Relat. Fields 134, 215–247 (2006). https://doi.org/10.1007/s00440-005-0427-6

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  • Received: 13 April 2003

  • Revised: 21 December 2004

  • Published: 03 May 2005

  • Issue Date: February 2006

  • DOI: https://doi.org/10.1007/s00440-005-0427-6

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Mathematics Subject Classifications (2000)

  • 35Q30
  • 60F05
  • 60H15
  • 60J05

Key words or phrases

  • Strong law of large numbers
  • Central limit theorem
  • Rate of convergence
  • Exponential mixing
  • Randomly forced PDE's
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