Related papers: Lectures on stochastic sewing with applications
A stochastic sewing lemma which is applicable for processes taking values in Banach spaces is introduced. Applications to additive functionals of fractional Brownian motion of distributional type are discussed.
These notes are based on a series of lectures given first at the University of Warwick in spring 2008 and then at the Courant Institute, Imperial College London, and EPFL. It is an attempt to give a reasonably self-contained presentation of…
Statistical physics courses typically employ abstract language that describes objects too small to be seen, making the topic challenging for students to understand. In this work, we introduce a simple experiment that allows conceptualizing…
We introduce a stochastic version of Gubinelli's sewing lemma, providing a sufficient condition for the convergence in moments of some random Riemann sums. Compared with the deterministic sewing lemma, adaptiveness is required and the…
This book covers a wide range of problems involving the applications of stochastic processes, stochastic calculus, large deviation theory, group representation theory and quantum statistics to diverse fields in dynamical systems,…
Stochastic processes offer a fundamentally different paradigm of dynamics than deterministic processes, the most prominent example of the latter being Newton's laws of motion. Here, we discuss in a pedagogical manner a simple and…
This is lecture notes on the course "Stochastic Processes". In this format, the course was taught in the spring semesters 2017 and 2018 for third-year bachelor students of the Department of Control and Applied Mathematics, School of Applied…
A tutorial review is given of some developments and applications of stochastic processes from the point of view of the practicioner physicist. The index is the following: 1.- Introduction 2.- Stochastic Processes 3.- Transient Stochastic…
We give a new take on the error analysis of approximations of stochastic differential equations (SDEs), utilizing and developing the stochastic sewing lemma of L\^e (2020). This approach allows one to exploit regularization by noise effects…
These notes provide a short, focused introduction to modelling stochastic gene expression, including a derivation of the master equation, the recovery of deterministic dynamics, birth-and-death processes, and Langevin theory. The notes were…
This is a set of lecture notes of a course on statistical physics and thermodynamics, which is oriented, to a certain extent, towards electrical engineering students. The main body of the lectures is devoted to statistical physics, whereas…
The aim of this textbook is to provide students with basic knowledge of stochastic models that may apply to telecommunications research areas, such as traffic modelling, resource provisioning and traffic management. These study areas are…
We study well-posedness of sweeping processes with stochastic perturbations generated by a fractional Brownian motion and convergence of associated numerical schemes. To this end, we first prove new existence, uniqueness and approximation…
This review maps developments in stochastic modeling, highlighting non-standard approaches and their applications to biology and epidemiology. It brings together four strands: (1) core models for systems that evolve with randomness; (2)…
Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest…
Many machine learning models require a training procedure based on running stochastic gradient descent. A key element for the efficiency of those algorithms is the choice of the learning rate schedule. While finding good learning rates…
We propose new limiting dynamics for stochastic gradient descent in the small learning rate regime called stochastic modified flows. These SDEs are driven by a cylindrical Brownian motion and improve the so-called stochastic modified…
We introduce stochastic normalizing flows, an extension of continuous normalizing flows for maximum likelihood estimation and variational inference (VI) using stochastic differential equations (SDEs). Using the theory of rough paths, the…
We develop a supervised-learning-based approach for monitoring and diagnosing texture-related defects in manufactured products characterized by stochastic textured surfaces that satisfy the locality and stationarity properties of Markov…
Stochastic efficiency is evaluated in five case studies: driven Brownian motion, effusion with a thermo-chemical and thermo-velocity gradient, a quantum dot and a model for information to work conversion. The salient features of stochastic…