A rigorous equation for the Cole-Hopf solution of the conservative KPZ equation

Abstract

A rigorous equation is stated and it is shown that the spatial derivative of the Cole-Hopf solution of the KPZ equation is a solution of this equation. The method of proof used to show that a process solves this equation is based on rather weak estimates so that this method has the advantage that it could be used to verify solutions of other highly singular SPDEs, too.

MAJOR REVISION, results and proofs are presented in a clearer way

References in corpus (2)

• Universality of KPZ equation
• A resolvent-type method for estimating time integrals of quadratic fluctuations in weakly asymmetric exclusion

Cited by in corpus (5)

• A stochastic Burgers equation from a class of microscopic interactions
• Regularization by noise and stochastic Burgers equations
• A resolvent-type method for estimating time integrals of quadratic fluctuations in weakly asymmetric exclusion
• Strong solution of the stochastic Burgers equation
• Renormalized-Generalized Solutions for the KPZ Equation