A new approach to Kolmogorov equations in infinite dimensions and applications to stochastic generalized Burgers equations (Q1876880)

The authors consider the so-called generalized stochastic Burgers equation (particular cases of this equation are classical stochastic reaction-diffusion equation and stochastic Burgers equation). The main aim of the paper is to solve the Kolmogorov equation, corresponding to the above-mentioned equation that is a partial differential equation in infinitely many variables. Its solution yields transition probabilities of a Markov process. It is shown that this process has weakly continuous sample paths and satisfies the generalized stochastic Burgers equation in the sense of Stroock-Varadhan's martingale problem. A new approach to investigation of the above-mentioned Kolmogorov equation is suggested.