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2024/2025

Научно-исследовательский семинар "Стохастический анализ и смежные вопросы 1"

Статус: Дисциплина общефакультетского пула
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.
Learning Objectives

Learning Objectives

  • -
Expected Learning Outcomes

Expected Learning Outcomes

  • ---
Course Contents

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
Assessment Elements

Assessment Elements

  • non-blocking Activity
  • non-blocking Activity
Interim Assessment

Interim Assessment

  • 2024/2025 2nd module
    𝑃, where 𝑃 is grade for participation in the research seminar
Bibliography

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

Authors

  • Иконописцева Юлия Вахтаногвна
  • KONAKOV VALENTIN DMITRIEVICH