[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 …
theory was greatly extended to various complicated setting and widely used in sciences and …
Algebraic renormalisation of regularity structures
We give a systematic description of a canonical renormalisation procedure of stochastic
PDEs containing nonlinearities involving generalised functions. This theory is based on the …
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 …
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 …
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 …
basic theoretical properties and recent numerical applications. The notes are split into two …
Phase behavior in thin films of cylinder-forming block copolymers
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 …
polybutadien-block-polystyrene triblock copolymer in thin films. The phase behavior can be …
Some recent progress in singular stochastic partial differential equations
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 …
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 …
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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SpringerLink Account Menu Find a journal Publish with us Track your research Search Cart …
SpringerLink Account Menu Find a journal Publish with us Track your research Search Cart …
[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 …
assumptions. In the latter case the measurability of solutions is also established. Conditions …