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

  • Armen Shirikyan


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.

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Laboratoire de MathématiquesUniversité de Paris-Sud XIOrsay CedexFrance

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