2017/01/25 by Massimiliano Gubinelli, Gubinelli, Massimiliano, Nicolas Perkowski +1
Economics, Econometrics and Finance · Engineering · #FOS: Mathematics #Financial Risk and Volatility Modeling #Fluid Dynamics and Turbulent Flows #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1701.07373
openalex publication_date 2017/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We review the formulation of the stochastic Burgers equation as a martingale problem. One way of understanding the difficulty in making sense of the equation is to note that it is a stochastic PDE with distributional drift, so we first review how to construct finite-dimensional diffusions with distributional drift. We then present the uniqueness result for the stationary martingale problem of [Gubinelli, Perkowski 2016], but we mainly emphasize the heuristic derivation and also we include a (very simple) extension of [Gubinelli, Perkowski 2016] to a non-stationary regime.