Infinite-dimensional paracontrolled distributions: the Burgers generator
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About this item
| Description: |
Perkowski, N
Thursday 6th September 2018 - 10:00 to 11:00 |
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| Created: | 2018-09-24 14:38 |
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| Collection: | Scaling limits, rough paths, quantum field theory |
| Publisher: | Isaac Newton Institute |
| Copyright: | Perkowski, N |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | Regularity structures, paracontrolled distributions and all that provide pathwise, deterministic tools to solve and study singular stochastic PDEs over finite-dimensional spaces. From a probabilistic point of view we would also like to understand the associated Kolmogorov backward equations, which can be interpreted as infinite-dimensional singular SPDEs. I will discuss on the example of the conservative stochastic Burgers equation how to construct a space of (para-) paracontrolled distributions in which the backward equation is well posed. As an application we obtain a martingale formulation and an alternative proof for the well-posedness of "energy solutions", without using the Cole-Hopf transform. The approach extends to some other singular SPDEs with Gaussian invariant measures and quadratic nonlinearities. This is joint work with Massimiliano Gubinelli. |
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