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Дополнительные главы теории вероятностей и математической статистики

Saturday, 26 December 2015 18:26

Спецсеминар для студентов 3 курса.
Читается в течении года, преподаватель Михаил Борисович Лагутин.

Обязательный для студентов кафедральной группы на 3-м курсе, продолжительность - 1 год.

Темы по теории вероятностей (осенний семестр):

Случайное блуждание и принцип отражения.
Возвращение блуждания и закон арксинуса.
Центральная предельная теорема и устойчивый закон.
Степенные ряды и производящие функции.
Блуждание на плоскости и в пространстве.
Блуждание по m-мерной решётке.
Условное математическое ожидание.
Марковское свойство.
Эргодичность.
Ветвящийся процесс с дискретным временем.
Предельные теоремы для ветвящегося процесса.
Распределения экстремальных значений.
Правильно меняющиеся функции и устойчивые законы.

Темы по математической статистике (весенний семестр):
Критерии согласия.
Критерии проверки однородности выборок.
Кластер-анализ.
Корреляционный анализ.
Регрессионный анализ.
Классификация с обучением.
Ядерные оценки плотности.
Модели авторегрессии и скользящего среднего для временных рядов.

Семинар проходит в форме докладов студентов.

Additional information