[图书][B] Mathematical control theory for stochastic partial differential equations

Q Lü, X Zhang - 2021 - Springer
It is well-known that Control Theory was founded by N. Wiener in 1948 ([349]). After that, this
theory was greatly extended to various complicated setting and widely used in sciences and …

Algebraic renormalisation of regularity structures

Y Bruned, M Hairer, L Zambotti - Inventiones mathematicae, 2019 - Springer
We give a systematic description of a canonical renormalisation procedure of stochastic
PDEs containing nonlinearities involving generalised functions. This theory is based on the …

KPZ reloaded

M Gubinelli, N Perkowski - Communications in Mathematical Physics, 2017 - Springer
We analyze the one-dimensional periodic Kardar–Parisi–Zhang equation in the language of
paracontrolled distributions, giving an alternative viewpoint on the seminal results of Hairer …

Neural signature kernels as infinite-width-depth-limits of controlled resnets

NM Cirone, M Lemercier… - … Conference on Machine …, 2023 - proceedings.mlr.press
Motivated by the paradigm of reservoir computing, we consider randomly initialized
controlled ResNets defined as Euler-discretizations of neural controlled differential …

A primer on the signature method in machine learning

I Chevyrev, A Kormilitzin - arXiv preprint arXiv:1603.03788, 2016 - arxiv.org
In these notes, we wish to provide an introduction to the signature method, focusing on its
basic theoretical properties and recent numerical applications. The notes are split into two …

Phase behavior in thin films of cylinder-forming block copolymers

A Knoll, A Horvat, KS Lyakhova, G Krausch… - Physical Review Letters, 2002 - APS
We have experimentally determined a phase diagram for cylinder-forming polystyrene-block-
polybutadien-block-polystyrene triblock copolymer in thin films. The phase behavior can be …

Some recent progress in singular stochastic partial differential equations

I Corwin, H Shen - Bulletin of the American Mathematical Society, 2020 - ams.org
Stochastic partial differential equations are ubiquitous in mathematical modeling. Yet, many
such equations are too singular to admit classical treatment. In this article we review some …

Stochastic quantization of Yang–Mills

I Chevyrev - Journal of Mathematical Physics, 2022 - pubs.aip.org
Yang–Mills (YM) theory plays an important role in the description of force-carrying particles
in the standard model. An important unsolved problem in mathematics is to show that YM …

[图书][B] Backward stochastic differential equations

J Zhang, J Zhang - 2017 - Springer
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[图书][B] Random Ordinary Differential Equations

X Han, PE Kloeden, X Han, PE Kloeden - 2017 - Springer
Existence and uniqueness theorems are given for RODEs under classical and Carathéodory
assumptions. In the latter case the measurability of solutions is also established. Conditions …