Pathwise analysis and parameter estimation for the stochastic Burgers equation
The solution to the stochastic Burgers equation with additive space-time white noise is analyzed in this work. The authors have contributed a first step towards the statistical inference of the stochastic Burgers equation. That is, they aim at estimating the drift parameter based on the discrete observation of the solution to stochastic Burgers equation on a finite interval. The estimators are constructed via the \(p\)-variations of the solution. The authors show that the solution to the Burgers equation admits a quadratic variation in space and a quartic variation in time and using this fact, they obtain the asymptotic properties (strong consistency, approximation error in \(L^p\)-norm) of the estimators. The main idea behind the proofs is to decompose the solution to stochastic Burgers equation into a sum of two stochastic processes, one of them coinciding with the solution to the linear stochastic heat equation (whose properties are well-known) and a second term which contains the nonlinear coefficient. The authors apply these results in order to estimate the drift parameter of solution to the Burgers equation by exploiting the behavior of the \(p\)-variations of the solution in time and in space.
scientific article; zbMATH DE number 7369575
scientific article