Related papers: Rough path theory and an introduction to rough par…
This chapter presents an introduction to robust statistics with applications of a chemometric nature. Following a description of the basic ideas and concepts behind robust statistics, including how robust estimators can be conceived, the…
In this note we prove some new results about the application of Wright functions of the first kind to solve fractional differential equations with variable coefficients. Then, we consider some applications of these results in order to…
In this note we briefly survey and propose some open problems related to isoparametric theory.
This paper surveys and discusses recent work adapting partial differential equation (PDE) models to discrete structures.
The main goal of these notes is to give an introduction to the mathematics of quantum noise and some of its applications in non-equilibrium statistical mechanics. We start with some reminders from the theory of classical stochastic…
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…
An elementary system leading to the notions of fractional integrals and derivatives is considered. Various physical situations whose description is associated with fractional differential equations of motion are discussed.
Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…
This paper investigates the convergence of Wong--Zakai approximations to regime-switching stochastic differential equations, generated by a collection of finite-variation approximations to Brownian motion. We extend the results of Nguyen…
We present sufficient conditions for finite controlled rho-variation of the covariance of Gaussian processes with stationary increments, based on concavity or convexity of their variance function. The motivation for this type of conditions…
Motivated by a problematic coming from mathematical finance, this paper is devoted to existing and additional results of continuity and differentiability of the It\^o map associated to rough differential equations. These regularity results…
Smooth manifolds are not the suitable context for trying to generalize the concept of rough paths on a manifold. Indeed, when one is working with smooth maps instead of Lipschitz maps and trying to solve a rough differential equation, one…
In this note, we review some of the recent developments in the well-posedness theory of nonlinear dispersive partial differential equations with random initial data.
Properties of partial integrals such as real and complex-valued polynomial, multiple polynomial, exponential, and conditional for ordinary differential systems are studied. The possibilities of constructing first integrals and last…
We develop in this article the principal constructive arguments used in quantum field theory, limiting us to bosonic theories, for which there does not exist any recent general presentation. The article is primarily written for…
These notes provide an introduction to a number of those topics in Classical Mechanics that are useful for field theory.
We prove well-posedness and rough path stability of a class of linear and semi-linear rough PDE's on $\mathbb{R}^d$ using the variational approach. This includes well-posedness of (possibly degenerate) linear rough PDE's in…
Background: Path integrals are a powerful tool for solving problems in quantum theory that are not amenable to a treatment by perturbation theory. Most path integral computations require an analytic continuation to imaginary time. While…
The goal of this review article is to provide a survey about the foundations of semilinear stochastic partial differential equations. In particular, we provide a detailed study of the concepts of strong, weak and mild solutions, establish…
We consider the rough differential equation $dY=f(Y)d\bm \om$ where $\bm \om=(\omega,\bbomega)$ is a rough path defined by a Brownian motion $\omega$ on $\RR^m$. Under the usual regularity assumption on $f$, namely $f\in C^3_b (\RR^d,…