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Author: Yichir Kakihara
Publisher: World Scientific
Published: 1997
Total Pages: 352
ISBN-13: 9789810230005
DOWNLOAD EBOOKA research-expository treatment of infinite-dimensional nonstationary stochastic processes (or time series) on a locally compact abelian group is provided with this book. Stochastic measures and scalar or operator bimeasures are fully discussed.
Author: Yuichiro Kakihara
Publisher: World Scientific
Published: 1997-02-27
Total Pages: 343
ISBN-13: 9814497894
DOWNLOAD EBOOKThis book provides a research-expository treatment of infinite-dimensional nonstationary stochastic processes or time series. Stochastic measures and scalar or operator bimeasures are fully discussed to develop integral representations of various classes of nonstationary processes such as harmonizable, V-bounded, Cramér and Karhunen classes and also the stationary class. Emphasis is on the use of functional, harmonic analysis as well as probability theory. Applications are made from the probabilistic and statistical points of view to prediction problems, Kalman filter, sampling theorems and strong laws of large numbers. Readers may find that the covariance kernel analysis is emphasized and it reveals another aspect of stochastic processes. This book is intended not only for probabilists and statisticians, but also for communication engineers.
Author: Yūichirō Kakihara
Publisher:
Published: 1997
Total Pages: 0
ISBN-13: 9789812779298
DOWNLOAD EBOOKThis book provides a research-expository treatment of infinite-dimensional nonstationary stochastic processes or time series. Stochastic measures and scalar or operator bimeasures are fully discussed to develop integral representations of various classes of nonstationary processes such as harmonizable, V-bounded, Cramer and Karhunen classes and also the stationary class. Emphasis is on the use of functional, harmonic analysis as well as probability theory. Applications are made from the probabilistic and statistical points of view to prediction problems, Kalman filter, sampling theorems and strong laws of large numbers. Readers may find that the covariance kernel analysis is emphasized and it reveals another aspect of stochastic processes. This book is intended not only for probabilists and statisticians, but also for communication engineers.
Author: Gregory F. Lawler
Publisher: CRC Press
Published: 2018-10-03
Total Pages: 249
ISBN-13: 1482286114
DOWNLOAD EBOOKEmphasizing fundamental mathematical ideas rather than proofs, Introduction to Stochastic Processes, Second Edition provides quick access to important foundations of probability theory applicable to problems in many fields. Assuming that you have a reasonable level of computer literacy, the ability to write simple programs, and the access to software for linear algebra computations, the author approaches the problems and theorems with a focus on stochastic processes evolving with time, rather than a particular emphasis on measure theory. For those lacking in exposure to linear differential and difference equations, the author begins with a brief introduction to these concepts. He proceeds to discuss Markov chains, optimal stopping, martingales, and Brownian motion. The book concludes with a chapter on stochastic integration. The author supplies many basic, general examples and provides exercises at the end of each chapter. New to the Second Edition: Expanded chapter on stochastic integration that introduces modern mathematical finance Introduction of Girsanov transformation and the Feynman-Kac formula Expanded discussion of Itô's formula and the Black-Scholes formula for pricing options New topics such as Doob's maximal inequality and a discussion on self similarity in the chapter on Brownian motion Applicable to the fields of mathematics, statistics, and engineering as well as computer science, economics, business, biological science, psychology, and engineering, this concise introduction is an excellent resource both for students and professionals.
Author: Bernard Keville
Publisher:
Published: 2004
Total Pages:
ISBN-13:
DOWNLOAD EBOOKAuthor: Yuichiro Kakihara
Publisher: World Scientific
Published: 2021-07-29
Total Pages: 539
ISBN-13: 9811211760
DOWNLOAD EBOOKThis is a development of the book entitled Multidimensional Second Order Stochastic Processes. It provides a research expository treatment of infinite-dimensional stationary and nonstationary stochastic processes or time series, based on Hilbert and Banach space-valued second order random variables. Stochastic measures and scalar or operator bimeasures are fully discussed to develop integral representations of various classes of nonstationary processes such as harmonizable, V-bounded, Cramér and Karhunen classes as well as the stationary class. A new type of the Radon-Nikodým derivative of a Banach space-valued measure is introduced, together with Schauder basic measures, to study uniformly bounded linearly stationary processes.Emphasis is on the use of functional analysis and harmonic analysis as well as probability theory. Applications are made from the probabilistic and statistical points of view to prediction problems, Kalman filter, sampling theorems and strong laws of large numbers. Generalizations are made to consider Banach space-valued stochastic processes to include processes of pth order for p ≥ 1. Readers may find that the covariance kernel is always emphasized and reveals another aspect of stochastic processes.This book is intended not only for probabilists and statisticians, but also for functional analysts and communication engineers.
Author: Richard Durrett
Publisher: Springer
Published: 2016-11-07
Total Pages: 282
ISBN-13: 3319456148
DOWNLOAD EBOOKBuilding upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding. Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatment of other topics useful for applications has been expanded. In addition, the ordering of topics has been improved; for example, the difficult subject of martingales is delayed until its usefulness can be applied in the treatment of mathematical finance.
Author: Samuel Karlin
Publisher: Gulf Professional Publishing
Published: 1981-05-12
Total Pages: 568
ISBN-13: 9780123986504
DOWNLOAD EBOOKAlgebraic methods in markov chains; Ratio theorems of transition probabilities and applications; Sums of independent random variables as a markov chain; Order statistics, poisson processes, and applications; Continuous time markov chains; Diffusion processes; Compouding stochastic processes; Fluctuation theory of partial sums of independent identically distributed random variables; Queueing processes.
Author: Vigirdas Mackevicius
Publisher: John Wiley & Sons
Published: 2013-02-07
Total Pages: 220
ISBN-13: 1118603249
DOWNLOAD EBOOKThis is an introduction to stochastic integration and stochastic differential equations written in an understandable way for a wide audience, from students of mathematics to practitioners in biology, chemistry, physics, and finances. The presentation is based on the naïve stochastic integration, rather than on abstract theories of measure and stochastic processes. The proofs are rather simple for practitioners and, at the same time, rather rigorous for mathematicians. Detailed application examples in natural sciences and finance are presented. Much attention is paid to simulation diffusion processes. The topics covered include Brownian motion; motivation of stochastic models with Brownian motion; Itô and Stratonovich stochastic integrals, Itô’s formula; stochastic differential equations (SDEs); solutions of SDEs as Markov processes; application examples in physical sciences and finance; simulation of solutions of SDEs (strong and weak approximations). Exercises with hints and/or solutions are also provided.
Author: Ronald Christensen
Publisher: Springer Science & Business Media
Published: 1991
Total Pages: 335
ISBN-13: 038797413X
DOWNLOAD EBOOKA companion volume to Plane answers to complex questions: the theory of linear models (1987), presenting six chapters with shallow treatments of very broad topics showing how the properties of three fundamental ideas from standard linear model theory can be used to examine multivariate, time series,
