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Большие уклонения

Saturday, 26 December 2015 18:26

Спецкурс для студентов 3-6 курсов, аспирантов

Представляет собой два полугодовых спецкурса по выбору кафедры "Большие уклонения: грубая асимпотика" и "Большие уклонения: точная асимптотика".
Лектор Александр Викторович Шкляев

В курсе освещается проблематика больших уклонений, грубая и точная асимптотика, классические результаты для случайного блуждания, марковских цепей, а также более общих случайных последовательностей.

Первый семестр курса посвящен локальной теореме Гнеденко и интегро-локальной теореме Стоуна, их обобщениям на случай больших уклонений, большим уклонениям сумм н.о.р. величин в случае распределений с тяжелыми хвостами, а также классической теории, связанной с грубой асимптотикой: теоремами Крамера и Гартнера-Эллиса. Также рассматриваются несколько приложений указанных результатов к статистике - исследуются критерии Неймана-Пирсона, хи-квадрат и отношения правдоподобий с точки зрения больших уклонений.

Второй семестр связан с более сложными задачами. В частности, рассматриваются аналоги теоремы Гартнера-Эллиса для точных уклонений и их приложения к статистике, точная асимптотика больших уклонений для цепей Маркова и ветвящихся процессов в случайной среде.

Для сдачи курсов необходимо сдать экзамен по теории на котором можно пользоваться рукописными лекциями.

Материалы курса можно найти в разделе Учебные материалы

Additional information