scholarly journals One-dimensional stochastic Burgers equation driven by Lévy processes

2007 ◽  
Vol 243 (2) ◽  
pp. 631-678 ◽  
Author(s):  
Z. Dong ◽  
T.G. Xu
Keyword(s):  
Lévy Processes ◽  
Burgers Equation ◽  
Levy Processes ◽  
One Dimensional ◽  
Stochastic Burgers Equation

scholarly journals On a stochastic Burgers equation with Dirichlet boundary conditions

2003 ◽  
Vol 2003 (43) ◽  
pp. 2735-2746 ◽  
Author(s):  
Ekaterina T. Kolkovska
Keyword(s):  
Weak Solution ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Burgers Equation ◽  
Martingale Problem ◽  
Weak Limit ◽  
Dirichlet Boundary Conditions ◽  
One Dimensional ◽  
Stochastic Burgers Equation ◽  
The One

We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.

scholarly journals Averaging principle for one dimensional stochastic Burgers equation

2018 ◽  
Vol 265 (10) ◽  
pp. 4749-4797 ◽  
Author(s):  
Zhao Dong ◽  
Xiaobin Sun ◽  
Hui Xiao ◽  
Jianliang Zhai
Keyword(s):  
Burgers Equation ◽  
Averaging Principle ◽  
One Dimensional ◽  
Stochastic Burgers Equation

scholarly journals Stochastic turbulence for Burgers equation driven by cylindrical Lévy process

2021 ◽  
Author(s):  
Shenglan Yuan ◽  
Dirk Blömker ◽  
Jinqiao Duan
Keyword(s):  
Kinematic Viscosity ◽  
Burgers Equation ◽  
Inviscid Limit ◽  
Regularity Of Solutions ◽  
One Dimensional ◽  
Stochastic Dynamical System ◽  
Qualitative And Quantitative ◽  
Stochastic Burgers Equation ◽  
Quantitative Properties ◽  
Turbulent Velocity Field

This work is devoted to investigating stochastic turbulence for the fluid flow in one-dimensional viscous Burgers equation perturbed by Lévy space-time white noise with the periodic boundary condition. We rigorously discuss the regularity of solutions and their statistical quantities in this stochastic dynamical system. The quantities include moment estimate, structure function and energy spectrum of the turbulent velocity field. Furthermore, we provide qualitative and quantitative properties of the stochastic Burgers equation when the kinematic viscosity [Formula: see text] tends towards zero. The inviscid limit describes the strong stochastic turbulence.

A multi-dimensional martingale for Markov additive processes and its applications

2000 ◽  
Vol 32 (02) ◽  
pp. 376-393 ◽  
Author(s):  
Søren Asmussen ◽  
Offer Kella
Keyword(s):  
Brownian Motion ◽  
Lévy Processes ◽  
Levy Processes ◽  
One Dimensional ◽  
Additive Processes ◽  
Motion Models ◽  
And Brownian Motion ◽  
Storage Processes ◽  
Reflecting Barriers ◽  
Markov Additive Processes

We establish new multidimensional martingales for Markov additive processes and certain modifications of such processes (e.g., such processes with reflecting barriers). These results generalize corresponding one-dimensional martingale results for Lévy processes. This martingale is then applied to various storage processes, queues and Brownian motion models.

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