2024/2025
Научно-исследовательский семинар "Стохастический анализ и смежные вопросы 1"
Статус:
Дисциплина общефакультетского пула
Кто читает:
Факультет математики
Где читается:
Факультет математики
Когда читается:
1, 2 модуль
Охват аудитории:
для всех кампусов НИУ ВШЭ
Язык:
английский
Кредиты:
3
Course Syllabus
Abstract
This research seminar will cover a wide range of problems related to stochastic analysis. Its aim is to present new developments in this field and to give students an opportunity to learn some modern concepts of stochastic analysis in connection with various mathematical area such as PDE’s optimization, optimal transport, statistics and machine learning. Special attention will be paid to applications in economics, finance, physics and other natural sciences. The talks will be given by the members of the laboratory of stochastic analysis and its applications (lsa.hse.ru), the guests of the laboratory, the stuff of the faculty of mathematics, as well as by students and postdocs.
Course Contents
- Transportation theory, Monge – Kantorovich problem (with applications in machine learning)
- Homogenisation theory for stochastic differential equations and slow-fast systems
- Discretisation and approximation schemes for stochastic differential equations
- Optimisation problems (with applications in machine learning)
- Non-parametric and semi-parametric statistics
- Applications of stochastic analysis in finance, insurance and economics
- Applications of stochastic analysis in physics, biology and other natural sciences
Bibliography
Recommended Core Bibliography
- A second course in stochastic processes, Karlin, S., 1981
- Introduction to nonparametric estimation, Tsybakov, A. B., 2009
Recommended Additional Bibliography
- Вероятность. Кн.1: Элементарная теория вероятностей. Математические основания. Предельные теоремы, Ширяев, А. Н., 2017
- Вероятность. Кн.2: Суммы и последовательности случайных величин - стационарные, мартингалы, марковские цепи, Ширяев, А. Н., 2017