Brillinger D.R., Time Series Data Analysis & Theory

New York – London – Sydney: John Wiley & Sons, Inc., 1964, - 130 pages. The book starts with a general introduction, and then a whole chapter on generating functions. The next four chapters deal with various kinds of processes in discrete time such as Markov chains and fandom walks. This is followed by the treatment of continuous-time processes, including such special applications as birth-and-death processes, queues, epidemics, etc. After th...

Cambridge University Press, 2007. - 480 pages. This treatment provides an exposition of discrete time dynamic processes evolving over an infinite horizon. Chapter 1 reviews some mathematical results from the theory of deterministic dynamical systems, with particular emphasis on applications to economics. The theory of irreducible Markov processes, especially Markov chains, is surveyed in Chapter 2. Equilibrium and long run stability of a dynami...

N.-Y., Springer Verlag, 1987. - 530p. Монография посвящена теории временных рядов, включая спектральные методы анализа, авторегрессию (ARMA и ARIMA), методам оценивания параметров, многомерным рядам, оцениванию спектров и т.п. Ориентирована на математика, работающего в этой области.

Springer, 1987. - 295 pages. This book is a self-contained treatment of the theory of probability, random processes. It is intended to lay solid theoretical foundations for advanced probability, that is, for measure and integration theory, and to develop in depth the long term time average behavior of measurements made on random processes with general output alphabets. Unlike virtually all texts on the topic, considerable space is devoted to pro...

Elsevier, 2011. - 410 Pages. Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. Models naturally render to statistical description, where random processes and fields express the input parameters and solutions. The fundamental problem of stochastic dynamics...

Berlin, Springer-Verlag, 2005. - 764p. Монография посвящена многомерному анализу временных рядов. Рассмотрены векторные авторегрессии конечного и бесконечного порядка, коинтегрированные процессы, структурные модели и одновременные уравнения и некоторые другие вопросы. Для научных работников и аспирантов в области математической статистики и теории случайных процессов, а также финансовой математики и других приложений.

Chapman & Hall/CRC, 2011. - 463 pages. Most existing books on evolution equations tend either to cover a particular class of equations in too much depth for beginners or focus on a very specific research direction. Thus, the field can be daunting for newcomers to the field who need access to preliminary material and behind-the-scenes detail. Taking an applications-oriented, conversational approach, Discovering Evolution Equations with Appli...

A John Wiley & Sons, Inc. , publication. 2009. Bayesian statistical decision theory. WinBUGS. Includes bibliographical references and index. 506 pages. Since the mid- 1980s, the development of widely accessible powerfbl computers and the implementation of Markov chain Monte Carlo (MCMC) methods have led to an explosion of interest in Bayesian statistics and modeling. This was followed by an extensive research for new Bayesian methodologies ge...

Singapore, World Scientific Publishing Co. Pte. Ltd., 2005. - 261 p. Книга посвящена анализу временных рядов при помощи методов нелинейной динамики, включая корреляционную размерность, экспоненту Ляпунова, энтропию, рассматривает методы оценки характеристик временных рядов, в том числе метод суррогатных данных, приводятся примеры использования этих подходов в задачах астрономии, медицины и финансов. Для научных работников и аспирантов.

This volume includes the five lecture courses given at the CIME-EMS School on "Stochastic Methods in Finance" held in Bressanone/Brixen, Italy 2003. It deals with innovative methods, mainly from stochastic analysis, that play a fundamental role in the mathematical modelling of finance and insurance: the theory of stochastic processes, optimal and stochastic control, stochastic differential equations, convex analysis and duality theory. Five topic...