Related papers: Stochastic Analysis Seminar on Filtering Theory
These lecture notes were written for the course 18.657, High Dimensional Statistics at MIT. They build on a set of notes that was prepared at Princeton University in 2013-14 that was modified (and hopefully improved) over the years.
Lecture notes on optimization for machine learning, derived from a course at Princeton University and tutorials given in MLSS, Buenos Aires, as well as Simons Foundation, Berkeley.
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…
These lecture notes are intended to cover some introductory topics in stochastic simulation for scientific computing courses offered by the IT department at Uppsala University, as taught by the author. Basic concepts in probability theory…
These are course notes on the application of SDEs to options pricing. The author was partially supported by NSF grant DMS-0739195.
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…
In these lecture notes, a selection of frequently required statistical tools will be introduced and illustrated. They allow to post-process data that stem from, e.g., large-scale numerical simulations (aka sequence of random experiments).…
These are lecture notes for a mini-course on stochastic sewing, taught at the University of Edinburgh and Beijing Institute of Technology in Spring/Summer 2025. The aim is to introduce the reader to stochastic sewing techniques and to show…
The article is a lightly edited version of my habilitation thesis at the University Wuerzburg. My aim is to give a self contained, if concise, introduction to the formal methods used when off-line learning in feedforward networks is…
This is a lecture note produced for DS-GA 3001.003 "Special Topics in DS - Causal Inference in Machine Learning" at the Center for Data Science, New York University in Spring, 2024. This course was created to target master's and PhD level…
This text is a survey of the general theory of stochastic processes, with a view towards random times and enlargements of filtrations. The first five chapters present standard materials, which were developed by the French probability school…
This document was prepared as part of the MT-LAB research centre. The research centre studies the Modelling of Information Technology and is a VKR Centre of Excellence funded for five years by the VILLUM Foundation. You can read more about…
These notes are based on a lecture delivered by NC on March 2021, as part of an advanced course in Princeton University on the mathematical understanding of deep learning. They present a theory (developed by NC, NR and collaborators) of…
This material was presented in a series of lectures at the Santa Fe Institute, the Los Alamos National Laboratory, and the University of New Mexico, during a one-month visit to the Santa Fe Institute, April 1995.
In January-March 2011, the Department of Mathematical Science at the University of Cincinnati held a Taft Research Seminar "Bellman function method in harmonic analysis." The seminar was made possible by a generous grant from the Taft…
These are lectures notes prepared for a series of seminars I am invited to give at Princeton Philosophy Department in November 2024. They cover the conceptual structure of quantum gravity, the relational interpretation of quantum mechanics,…
This manuscript presents shortly the results obtained by participants of the scientific seminar which is held more than twenty years under leadership of the author at Donetsk University. In the list of references main publications are…
These are the lecture notes for an advanced Ph.D. level course I taught in Spring'02 at the C.N. Yang Institute for Theoretical Physics at Stony Brook. The course primarily focused on an introduction to stochastic calculus and derivative…
The 2008 Workshop on Algorithms for Modern Massive Data Sets (MMDS 2008), sponsored by the NSF, DARPA, LinkedIn, and Yahoo!, was held at Stanford University, June 25--28. The goals of MMDS 2008 were (1) to explore novel techniques for…
These notes gather recent results on robust statistical learning theory. The goal is to stress the main principles underlying the construction and theoretical analysis of these estimators rather than provide an exhaustive account on this…