arXiv:1810.12014math.PR
The infinitesimal generator of the stochastic Burgers equation
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Abstract
We develop a martingale approach for a class of singular stochastic PDEs of Burgers type (including fractional and multi-component Burgers equations) by constructing a domain for their infinitesimal generators. It was known that the domain must have trivial intersection with the usual cylinder test functions, and to overcome this difficulty we import some ideas from paracontrolled distributions to an infinite dimensional setting in order to construct a domain of controlled functions. Using the new domain, we are able to prove existence and uniqueness for the Kolmogorov backward equation and the martingale problem. We also extend the uniqueness result for "energy solutions" of the stochastic Burgers equation of [GP18a] to a wider class of equations.
I generally use TeXmacs for notes, derivations, lectures, articles, all, of course. Most of my papers in the last 7 years, around 15 and all my lectures in the same period, circa 2 courses a year. More in detail, all these papers are been written completely in TeXmacs and then…
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