Martingale problems for some singular SPDEs

Abstract: Most techniques for solving singular SPDEs, such as regularity structures, are based on pathwise calculus. It would be interesting to study singular SPDEs from a more probabilistic perspective, for example via the martingale problem. In general that is a too difficult problem at the moment, but there are some equations for which we can do this. I will explain the ideas on the example of the conservative stochastic Burgers equation and indicate how to extend the results to a larger class of equations that share a similar structure. A novelty of this approach is that it allows to prove (weak) well-posedness for some scaling critical singular SPDEs. Based on works with Massimiliano Gubinelli and Lukas Gräfner.

analysis of PDEsprobability

Audience: researchers in the discipline

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Stochastic PDEs and their friends

Series comments: We are organizing a three day online workshop devoted to recent developments in SPDEs and related topics. Please complete the registration form at forms.gle/G9Xw942iVNNgB4SLA if you would like to take part in the conference.

Confirmed speakers:

Yuri BAKHTIN (NYU)

Ajay CHANDRA (Imperial)

Dan CRISAN (Imperial)

Nina HOLDEN (ETH Zurich)

Kostantin KHANIN (U Toronto)

Davar KHOSHNEVISAN (University of Utah)

Nicolai KRYLOV (University of Minnesota)

Jonathan MATTINGLY (Duke)

Leonid MYTNIK (Technion)

Nicolas PERKOWSKI (Free U Berlin)

Ellen POWELL (Durham University)

Jeremy QUASTEL (U Toronto)

Daniel REMENIK (Universidad de Chile)

Armen SHIRIKYAN (University of Cergy-Pontoise)

Gigliola STAFFILANI (MIT)

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