Stochastic Burgers' equation on the real line: regularity and moment estimates. Issue 7 (3rd October 2018)

• Record Type: Journal Article
• Authors: Lewis, Peter; Nualart, David
• Is Part Of: Stochastics. Volume 90:Issue 7(2018)
• Page Start: 1053
• Page End: 1086
• Publication Date: 2018-10-03
• Subjects: Stochastic Burgers' equation -- Feynman–Kac representation -- space-time white noise -- heat kernel; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2018.1478834
• Languages: English
• ISSNs: 1744-2508

Abstract

ABSTRACT: In this project, we investigate the stochastic Burgers' equation with multiplicative space-time white noise on an unbounded spatial domain. We give a random field solution to this equation by defining a process via a kind of Feynman–Kac representation which solves a stochastic partial differential equation such that its Hopf–Cole transformation solves Burgers' equation. Finally, we obtain Hölder regularity and moment estimates for the solution to Burgers' equation.