Parameter identification for stochastic burgers' flows via parabolic rescaling

The paper presents a systematic study of classical statistical inference problems (parameter estimation and hypothesis testing) for random fields arising as solutions of the one-dimensional nonlinear diffusion equation with random initial data (the Burgers' turbulence problem). This nonlinear, hydrodynamic-type partial differential equation is an ubiquitous model in physics and engineering. This work can be seen as part of a larger program of developing statistical inference tools for complex stochastic flows governed by nontrivial, physically constrained dynamics.