A Markov jump process approximation of the stochastic Burgers equation

2004/08/24 by Christoph Gugg, Gugg, Christoph, Jinqiao Duan +1
Economics, Econometrics and Finance · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.DS #math.PR

paper · pdf · doi:10.48550/arxiv.math/0408323

in press

arxiv created 2004/08/24 · openalex publication_date 2004/08/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the stochastic Burgers equation \dnachdt ψ(t,r) = Δψ(t,r) + ∇ ψ²(t,r)+√(γψ(t,r)) η(t,r) with periodic boundary conditions, where t ≥ 0, r ∈ [0,1], and η is some space-time white noise. A certain Markov jump process is constructed to approximate a solution of this equation.

Related

• Stochastic Burgers' Equation on the Real Line: Regularity and Moment Estimates
• Approximations of Stochastic Partial Differential Equations
• Estimate for P_tD for the stochastic Burgers equation
• Introduction à l'équation de Burgers stochastique et à la burgulence
• Asymptotics for stochastic Burgers equation with jumps