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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 1999-6
January 1999

Parameter identification for stochastic Burgers flows via parabolic rescaling


Nikolai N. Leonenko, Wojbor A. Woyczynski


The paper presents a systematic study of classical statistical inference problems (parameter estimation and hypothesis testing) for random fields arising as solutions of the one-dimensional nonlinear diffusion equation with random initial data (the Burgers turbulence problem). This nonlinear, hydrodynamic-type partial differential equation is an ubiquitous model in physics and engineering. This work can be seen as part of a larger program of developing statistical inference tools for complex stochastic flows governed by nontrivial physically constrained dynamics.

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This paper has now been published in Probability and Mathematical Statistics (2001) 21, 1, 1-55.