• Corpus ID: 119127668

# Analysis and Probability on Infinite-Dimensional Spaces

@article{Eldredge2016AnalysisAP,
title={Analysis and Probability on Infinite-Dimensional Spaces},
author={Nathaniel Eldredge},
journal={arXiv: Probability},
year={2016}
}
These lecture notes contain an introduction to some of the fundamental ideas and results in analysis and probability on infinite-dimensional spaces, mainly Gaussian measures on Banach spaces. They originated as the notes for a topics course at Cornell University in 2011.
16 Citations
The aim of this article is to generalize the Lebesgue integration theory to $\mathbb{R}^{\mathbb{N}}$ within a preliminary measure theory, just as an extension of finite dimensional Lebesgue
• Mathematics
• 2019
Motivated by numerous questions in random geometry, given a smooth manifold $M$, we approach a systematic study of the differential topology of Gaussian Random Fields (GRF) $X:M\to \mathbb{R}^k$,
We consider the basic problem of approximating Nash equilibria in noncooperative games. For monotone games, we design continuous time ﬂows which converge in an averaged sense to Nash equilibria. We
These notes were inspired by the course ''Quantum Field Theory from a Functional Integral Point of View'' given at the University of Zurich in Spring 2017 by Santosh Kandel. We describe Feynman's
• Mathematics
• 2017
Consider a separable Banach space $\mathcal{W}$ supporting a non-trivial Gaussian measure $\mu$. The following is an immediate consequence of the theory of Gaussian measure on Banach spaces: there
• Computer Science
ArXiv
• 2022
This work generalizes diffusion models to operate directly in function space by developing the foundational theory for such models in terms of Gaussian measures on Hilbert spaces and developing methods for diffusion generative modeling in Sobolev spaces.
• Mathematics
ArXiv
• 2022
The traditional information-theoretic methods are lifted to infinite-dimensional spaces and formulate various control and filtering systems uniformly as noisy communication channels and the general trade-offs are computed by resorting to the Stratonovich-Kushner equation.
• Computer Science
NIPS
• 2017
A novel variational Gaussian process model that decouples the representation of mean and covariance functions in reproducing kernel Hilbert space is proposed and it is shown that this new parametrization generalizes previous models and makes the adoption of large-scale expressiveGaussian process models possible.

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The aim of this book is to give a rigorous introduction for the graduate students to Analysis on Wiener space, a subject which has grown up very quickly these recent years under the new impulse of
Gaussian measures in Banach spaces.- Equivalence and orthogonality of Gaussian measures.- Some results about abstract Wiener space.
Analysis on the Wiener space.- Regularity of probability laws.- Anticipating stochastic calculus.- Transformations of the Wiener measure.- Fractional Brownian motion.- Malliavin Calculus in finance.-
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In real Hilbert space H there is a finitely additive measure n on the ring of sets defined by finitely many linear conditions, which is analogous to the normal distribution in the finite-dimensional
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We construct a hereditarily indecomposable Banach space with dual isomorphic to $\ell_1$. Every bounded linear operator on this space has the form $\lambda I+K$ with $\lambda$ a scalar and $K$
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We construct a hereditarily indecomposable Banach space with dual space isomorphic to ℓ1. Every bounded linear operator on this space is expressible as λI + K, with λ a scalar and K compact.
extends in a well known way to a measure v on the Borel sets of L, which is independent of the choice of basis yt,---,y„ used in constructing it and depends only on the mapping F. Every probability
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After Poincare inequalities, logarithmic Sobolev inequalities are amongst the most studied functional inequalities for semigroups. They contain much more information than Poincare inequalities, and
1 Preliminaries of Measure Theory Denition 1 F P ( ) is said to be an algebra if (1) 2 F (2) A;B 2 F implies A S B 2 F (3) A 2 F implies AC 2 F . F is said to be a semialgebra or semi-ring is (1) ;?
The classical descriptive set theory is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can download it instantly.