Related papers: Analysis on Wiener Space and Applications
The Mat\'ern model has been a cornerstone of spatial statistics for more than half a century. More recently, the Mat\'ern model has been central to disciplines as diverse as numerical analysis, approximation theory, computational…
These lectures introduce key concepts in probability and statistical inference at a level suitable for graduate students in particle physics. Our goal is to paint as vivid a picture as possible of the concepts covered.
In these informal lecture notes we outline different approaches used in doing calculations involving the Dirac equation in curved spacetime. We have tried to clarify the subject by carefully pointing out the various conventions used and by…
These lectures notes give an introduction to the fast developing area of research dealing with perturbative descriptions of the gravitational instability in an expanding universe. I just sketch the outlines of some proofs, and many…
The purpose of this work is to extend the formalism of stochastic calculus to the case of spaces with local anisotropy (modeled as vector bundles with compatible nonlinear and distinguished connections and metric structures and containing…
This paper presents a novel generic asymptotic expansion formula of expectations of multidimensional Wiener functionals through a Malliavin calculus technique. The uniform estimate of the asymptotic expansion is shown under a weaker…
In this article we introduce a new method for the construction of unique strong solutions of a larger class of stochastic delay equations driven by a discontinuous drift vector field and a Wiener process. The results obtained in this paper…
This paper presents an extended version of lecture notes for an introductory course on Berkovich analytic spaces that I gave in 2010 at Summer School "Berkovich spaces" at Institut de Mathmatiques de Jussieu.
Variational-hemivariational inequalities are an area full of interesting and challenging mathematical problems. The area can be viewed as a natural extension of that of variational inequalities. Variational-hemivariational inequalities are…
This book provides a gentle introduction to fractional Sobolev spaces, which play a central role in the calculus of variations, partial differential equations, and harmonic analysis. The first part deals with fractional Sobolev spaces of…
This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
These lectures introduce the basic ideas and practices of statistical analysis for particle physicists, using a real-world example to illustrate how the abstractions on which statistics is based are translated into practical application.
In this paper various properties of global and local changes of variables as well as properties of canonical transforms are investigated on modulation and Wiener amalgam spaces. We establish several relations among localisations of…
We study a (relativistic) Wiener process on a complexified (pseudo-)Riemannian manifold. Using Nelson's stochastic quantization procedure, we derive three equivalent descriptions for this problem. If the process has a purely real quadratic…
One of the core problems of modern statistics is to approximate difficult-to-compute probability densities. This problem is especially important in Bayesian statistics, which frames all inference about unknown quantities as a calculation…
The goal of these notes is to provide an informal introduction to Gromov-Witten theory with an emphasis on its role in counting curves in surfaces. These notes are based on a talk given at the Fields Institute during a week-long conference…
This set of lecture notes constitutes the free textbook project I initiated towards the end of Summer 2015, while preparing for the Fall 2015 Analytical Methods in Physics course I taught to upper level undergraduates at the University of…
In [NP09a], Nourdin and Peccati established a neat characterization of Gamma approximation on a fixed Wiener chaos in terms of convergence of only the third and fourth cumulants. In this paper, we investigate the rate of convergence in…
Rejoinder to ``Analysis of variance--why it is more important than ever'' by A. Gelman [math.ST/0504499]