Notice: Array to string conversion in /var/vhosts/new/department/matstat/libraries/joomla/registry/registry.php on line 342 Notice: Array to string conversion in /var/vhosts/new/department/matstat/libraries/joomla/registry/registry.php on line 342 Deprecated: iconv_set_encoding(): Use of iconv.internal_encoding is deprecated in /var/vhosts/new/department/matstat/libraries/joomla/string/string.php on line 28 Deprecated: iconv_set_encoding(): Use of iconv.input_encoding is deprecated in /var/vhosts/new/department/matstat/libraries/joomla/string/string.php on line 29 Deprecated: iconv_set_encoding(): Use of iconv.output_encoding is deprecated in /var/vhosts/new/department/matstat/libraries/joomla/string/string.php on line 30 Notice: Array to string conversion in /var/vhosts/new/department/matstat/libraries/joomla/registry/registry.php on line 342 Notice: Array to string conversion in /var/vhosts/new/department/matstat/libraries/joomla/registry/registry.php on line 342 Notice: Array to string conversion in /var/vhosts/new/department/matstat/libraries/joomla/registry/registry.php on line 342 Notice: Array to string conversion in /var/vhosts/new/department/matstat/libraries/joomla/registry/registry.php on line 342 Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /var/vhosts/new/department/matstat/libraries/joomla/filter/input.php on line 652 Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /var/vhosts/new/department/matstat/libraries/joomla/filter/input.php on line 654 Сайт кафедры математической статистики и случайных процессов
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Спецкурсы и спецсеминары

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Нестандартные задачи теории вероятностей

Лекторы с.н.с А.В. Шкляев и асс. О.П. Орлов. Читается в осеннем семестре. Курс по выбору кафедры.

К сожалению, курс теории вероятностей в четвертом семестре значительно перегружен и многие темы даются там на достаточно поверхностном уровне. Представленный курс предлагает заполнить ряд пробелов в этом направлении. В курсе более глубоко рассматриваются некоторые вопросы: подсчет математических ожиданий как стандартными (линейность, рекуррентные соотношения) так и более продвинутыми (мартингальный подход) методами, геометрическая вероятность (в частности метод Крофтона и его обобщения), вероятностный метод в невероятностных задачах, метод одного вероятностного пространства и другие полезные подходы, которые позволяют решать менее стандартные задачи, чем те, которые встречаются в общем курсе.

Теория мартингалов и стохастическое интегрирование

Лектор д.ф.-м.н. В.А. Лебедев. Читается в осеннем семестре, курс по выбору кафедры.

В спецкурсе исследуется достаточно обширный класс случайных процессов (мартингалы и их обобщения) и на этой основе развивается современная теория стохастического интегрирования.

Линейные операторы и марковские цепи

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Курс читается с 2021 года ассистентом кафедры Г.А. Бакаем.

В данном курсе представлена теория марковских цепей, которая начинается с простых и осязаемых понятий, таких как матрицы, собственные векторы, но корнями уходит в глубокую и удивительную теорию линейных операторов на бесконечномерных пространствах. Стартуя с этих позиций слушатели двигаются в сторону понятия стационарной последовательности, и получают предельные теоремы для сумм функционалов от марковской цепи, включающие большие уклонения для данных последовательностей

Современные подходы к проверке однородности и независимости

Parent Category: Спецкурсы и спецсеминары

Спецкурс для студентов 3-6 курсов, аспирантов

Представляет собой полугодовой спецкурс по выбору кафедры. Лектор Александр Викторович Шкляев

В курсе освещаются подходы для проверки данных двух видов гипотез.

В последние 15 лет был получен большой спектр подходов к проверке гипотезы однородности и гипотезы независимости. Мы сформулируем общий подход к рассмотрению критериев независимости и однородности и рассмотрим наиболее удачные версии, стартуя с классических критериев Стьюдента, Манна-Уитни, Пирсона, Спирмена, Кенделла, хи-квадрат и продолжая критериями BWS, MMD, Energy Test, Dcov, HSIC, HHG и прочими. Мы рассмотрим как прикладной аспект (сравним критерии на ряде популярных массивов данных), так и теоретический, построив, в частности, столь важную в различных целях конструкцию RKHS.

Для сдачи курса нужно сдать экзамен по теории. Сложность экзамена значительно варьируется в зависимости от выполнения домашних заданий.

Нестандартные задачи теории вероятностей

Parent Category: Спецкурсы и спецсеминары

Руководители: А.В. Шкляев и О.И. Орлов

Читается в осеннем семестре с 2019 года.

Курс посвящен углубленному изучению некоторых тем с помощью более сложных задач олимпиадного типа.

Курс проходит в формате листочков с задачами, предваряемых теорией. Для сдачи курса необходимо сдать не менее 4 задач по 70% листков.

Текущие материалы курса можно отыскать в разделе Учебные материалы

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  1. Введение в теорию ветвящихся процессов
  2. Избранные вопросы математической статистики
  3. Параметрическая статистика
  4. Анализ временных рядов

Subcategories

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