Liptser Robert S., Shiryaev Albert N., Aries B. Statistics of Random Processes / I. General Theory 9783540639299

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Автор: Liptser Robert S., Shiryaev Albert N., Aries B.
Название: Statistics of Random Processes / I. General Theory
Перевод названия: Роберт Липстер: Статистика случайных процессов. Общая теория
ISBN: 9783540639299
Издательство: Springer
Классификация:

Вероятность и статистика

Прикладная математика

ISBN-10: 3540639292
Обложка/Формат: Hardback
Страницы: 442
Вес: 0.81 кг.
Дата издания: 06.11.2000
Серия: Stochastic Modelling and Applied Probability
Язык: English
Издание: 2 rev ed
Размер: 24.16 x 16.56 x 3.02
Читательская аудитория: Postgraduate, research & scholarly
Ссылка на Издательство: Link
Рейтинг:
Поставляется из: Германии
Описание: The subject of these two volumes is non-linear filtering (prediction and smoothing) theory and its application to the problem of optimal estimation, control with incomplete data, information theory, and sequential testing of hypothesis. The book is not only addressed to mathematicians but should also serve the interests of other scientists who apply probabilistic and statistical methods in their work. The theory of martingales presented in the book has an independent interest in connection with problems from financial mathematics. In the second edition, the authors have made numerous corrections, updating every chapter, adding two new subsections devoted to the Kalman filter under wrong initial conditions, as well as a new chapter devoted to asymptotically optimal filtering under diffusion approximation. Moreover, in each chapter a comment is added about the progress of recent years.
Дополнительное описание: Формат: 235x155
Круг читателей: Students and researchers
Ключевые слова: Conditionally Gaussian
Filtering
Incomplete Data Control
Martingale
Point Process
Язык: rus
Издание: 2nd rev. and exp. ed.
Оглавление: Essentials of probability theory and mathematical statistics.- Martingales and related processes.- Martingales and supermartingales: continuous time.- The Wiener process, the stochastic integral over the Wiener process, and stochastic differential equations.- Square integrable martingales, and structure of the functionals on a Wiener process.- Nonnegative supermartingales and martingales, and the Girsanovs theorem.- Absolute continuity of measures corresponding to the Ito processes and processes of diffusion type.- General equations of optimal nonlinear filtering, interpolation and extrapolation of partially observable random processes.- Optimal filtering, interpolation and extrapolation of Markov processes with countable number of states.- Optimal linear nonstationary filtering.

Statistics of Random Processes / I. General Theory, Liptser Robert S., Shiryaev Albert N., Aries B.