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Burgers' turbulence problem with linear or quadratic external potential

Part of: Stochastic processes Stochastic analysis Inference from stochastic processes

Published online by Cambridge University Press:  14 July 2016

O. E. Barndorff-Nielsen  and
N. N. Leonenko
O. E. Barndorff-Nielsen*
Affiliation:
University of Aarhus
N. N. Leonenko*
Affiliation:
Cardiff University
*
∗ Postal address: Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, K-8000 Aarhus C, Denmark. Email address: oebn@imf.au.dk
∗∗ Postal address: Cardiff School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4AG, UK. Email address: leonenkon@cardiff.ac.uk
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Abstract

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We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions.

Keywords

Inhomogeneous Burgers equationOrnstein-Uhlenbeck-type processlinear potentialquadratic potentialrandom initial conditionstationary processshort-range dependencelong-range dependenceinfinitely divisible distributionnormal inverse Gaussian distribution

MSC classification

Primary: 62M40: Random fields; image analysis 62M15: Spectral analysis 60H15: Stochastic partial differential equations 60G60: Random fields

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 2 , June 2005 , pp. 550 - 565
Copyright
© Applied Probability Trust 2005 

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