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Author: P. Hall Publisher: Academic Press ISBN: 1483263223 Category : Mathematics Languages : en Pages : 321
Book Description
Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior that has wide applications. The book explains the thesis that martingale theory is central to probability theory, and also examines the relationships between martingales and processes embeddable in or approximated by Brownian motion. The text reviews the martingale convergence theorem, the classical limit theory and analogs, and the martingale limit theorems viewed as the rate of convergence results in the martingale convergence theorem. The book explains the square function inequalities, weak law of large numbers, as well as the strong law of large numbers. The text discusses the reverse martingales, martingale tail sums, the invariance principles in the central limit theorem, and also the law of the iterated logarithm. The book investigates the limit theory for stationary processes via corresponding results for approximating martingales and the estimation of parameters from stochastic processes. The text can be profitably used as a reference for mathematicians, advanced students, and professors of higher mathematics or statistics.
Author: P. Hall Publisher: Academic Press ISBN: 1483263223 Category : Mathematics Languages : en Pages : 321
Book Description
Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior that has wide applications. The book explains the thesis that martingale theory is central to probability theory, and also examines the relationships between martingales and processes embeddable in or approximated by Brownian motion. The text reviews the martingale convergence theorem, the classical limit theory and analogs, and the martingale limit theorems viewed as the rate of convergence results in the martingale convergence theorem. The book explains the square function inequalities, weak law of large numbers, as well as the strong law of large numbers. The text discusses the reverse martingales, martingale tail sums, the invariance principles in the central limit theorem, and also the law of the iterated logarithm. The book investigates the limit theory for stationary processes via corresponding results for approximating martingales and the estimation of parameters from stochastic processes. The text can be profitably used as a reference for mathematicians, advanced students, and professors of higher mathematics or statistics.
Author: David Williams Publisher: Cambridge University Press ISBN: 9780521406055 Category : Mathematics Languages : en Pages : 274
Book Description
This is a masterly introduction to the modern, and rigorous, theory of probability. The author emphasises martingales and develops all the necessary measure theory.
Author: B. Ramdas Bhat Publisher: New Age International ISBN: 9788122411898 Category : Probabilities Languages : en Pages : 348
Book Description
The Book Continues To Cover The Syllabus Of A One-Year Course On Probability Theory. The Rigorous Axiomatic Approach Continues To Be Followed. For Those Who Plan To Apply Probability Models In Their Chosen Areas The Book Will Provide The Necessary Foundation. For Those Who Want To Proceed To Work In The Area Of Stochastic Processes, The Present Work Will Provide The Necessary Preliminary Background. It Can Be Used By Probabilists, Statisticians And Mathematicians. In The Present Revised Edition Many Concepts Have Been Elaborated. Clarifications Are Given For A Number Of Steps In The Proofs Of Results Derived. Additional Examples And Problems Are Given At The End Of Different Chapters. An Additional Preliminary Chapter Has Been Added So That Students Can Recapitulate The Topics Normally Covered In The Undergraduate Courses. It Also Forms The Foundation For Topics Covered In The Remaining Chapters. The Third Edition Incorporates The Suggestions For Improvements Received By The Author When The Earlier Editions Were In Circulation. With The Additional Features And Most Of The Errors Weeded Out, The Book Is Hoped To Become More Useful In The Hands Of Students And Teachers.
Author: James Davidson Publisher: Oxford University Press ISBN: 0192658808 Category : Business & Economics Languages : en Pages : 796
Book Description
Stochastic Limit Theory, published in 1994, has become a standard reference in its field. Now reissued in a new edition, offering updated and improved results and an extended range of topics, Davidson surveys asymptotic (large-sample) distribution theory with applications to econometrics, with particular emphasis on the problems of time dependence and heterogeneity. The book is designed to be useful on two levels. First, as a textbook and reference work, giving definitions of the relevant mathematical concepts, statements, and proofs of the important results from the probability literature, and numerous examples; and second, as an account of recent work in the field of particular interest to econometricians. It is virtually self-contained, with all but the most basic technical prerequisites being explained in their context; mathematical topics include measure theory, integration, metric spaces, and topology, with applications to random variables, and an extended treatment of conditional probability. Other subjects treated include: stochastic processes, mixing processes, martingales, mixingales, and near-epoch dependence; the weak and strong laws of large numbers; weak convergence; and central limit theorems for nonstationary and dependent processes. The functional central limit theorem and its ramifications are covered in detail, including an account of the theoretical underpinnings (the weak convergence of measures on metric spaces), Brownian motion, the multivariate invariance principle, and convergence to stochastic integrals. This material is of special relevance to the theory of cointegration. The new edition gives updated and improved versions of many of the results and extends the coverage of many topics, in particular the theory of convergence to alpha-stable limits of processes with infinite variance.
Author: Zhengyan Lin Publisher: World Scientific ISBN: 9814447706 Category : Business & Economics Languages : en Pages : 185
Book Description
Weak convergence of stochastic processes is one of most important theories in probability theory. Not only probability experts but also more and more statisticians are interested in it. In the study of statistics and econometrics, some problems cannot be solved by the classical method. In this book, we will introduce some recent development of modern weak convergence theory to overcome defects of classical theory.Contents: "The Definition and Basic Properties of Weak Convergence: "Metric SpaceThe Definition of Weak Convergence of Stochastic Processes and Portmanteau TheoremHow to Verify the Weak Convergence?Two Examples of Applications of Weak Convergence"Convergence to the Independent Increment Processes: "The Basic Conditions of Convergence to the Gaussian Independent Increment ProcessesDonsker Invariance PrincipleConvergence of Poisson Point ProcessesTwo Examples of Applications of Point Process Method"Convergence to Semimartingales: "The Conditions of Tightness for Semimartingale SequenceWeak Convergence to SemimartingaleWeak Convergence to Stochastic Integral I: The Martingale Convergence ApproachWeak Convergence to Stochastic Integral II: Kurtz and Protter's ApproachStable Central Limit Theorem for SemimartingalesAn Application to Stochastic Differential EquationsAppendix: The Predictable Characteristics of Semimartingales"Convergence of Empirical Processes: "Classical Weak Convergence of Empirical ProcessesWeak Convergence of Marked Empirical ProcessesWeak Convergence of Function Index Empirical ProcessesWeak Convergence of Empirical Processes Involving Time-Dependent dataTwo Examples of Applications in Statistics Readership: Graduate students and researchers in probability & statistics and econometrics.
Author: Narahari U Prabhu Publisher: World Scientific Publishing Company ISBN: 9813106956 Category : Mathematics Languages : en Pages : 356
Book Description
Most introductory textbooks on stochastic processes which cover standard topics such as Poisson process, Brownian motion, renewal theory and random walks deal inadequately with their applications. Written in a simple and accessible manner, this book addresses that inadequacy and provides guidelines and tools to study the applications. The coverage includes research developments in Markov property, martingales, regenerative phenomena and Tauberian theorems, and covers measure theory at an elementary level.
Author: Jean Jacod Publisher: Springer Science & Business Media ISBN: 3662025140 Category : Mathematics Languages : en Pages : 620
Book Description
Initially the theory of convergence in law of stochastic processes was developed quite independently from the theory of martingales, semimartingales and stochastic integrals. Apart from a few exceptions essentially concerning diffusion processes, it is only recently that the relation between the two theories has been thoroughly studied. The authors of this Grundlehren volume, two of the international leaders in the field, propose a systematic exposition of convergence in law for stochastic processes, from the point of view of semimartingale theory, with emphasis on results that are useful for mathematical theory and mathematical statistics. This leads them to develop in detail some particularly useful parts of the general theory of stochastic processes, such as martingale problems, and absolute continuity or contiguity results. The book contains an elementary introduction to the main topics: theory of martingales and stochastic integrales, Skorokhod topology, etc., as well as a large number of results which have never appeared in book form, and some entirely new results. It should be useful to the professional probabilist or mathematical statistician, and of interest also to graduate students.
Author: Allan Gut Publisher: Springer Science & Business Media ISBN: 1475719922 Category : Mathematics Languages : en Pages : 208
Book Description
My first encounter with renewal theory and its extensions was in 1967/68 when I took a course in probability theory and stochastic processes, where the then recent book Stochastic Processes by Professor N.D. Prabhu was one of the requirements. Later, my teacher, Professor Carl-Gustav Esseen, gave me some problems in this area for a possible thesis, the result of which was Gut (1974a). Over the years I have, on and off, continued research in this field. During this time it has become clear that many limit theorems can be obtained with the aid of limit theorems for random walks indexed by families of positive, integer valued random variables, typically by families of stopping times. During the spring semester of 1984 Professor Prabhu visited Uppsala and very soon got me started on a book focusing on this aspect. I wish to thank him for getting me into this project, for his advice and suggestions, as well as his kindness and hospitality during my stay at Cornell in the spring of 1985. Throughout the writing of this book I have had immense help and support from Svante Janson. He has not only read, but scrutinized, every word and every formula of this and earlier versions of the manuscript. My gratitude to him for all the errors he found, for his perspicacious suggestions and remarks and, above all, for what his unusual personal as well as scientific generosity has meant to me cannot be expressed in words.
Author: M. M. Rao Publisher: Elsevier ISBN: 0080925367 Category : Mathematics Languages : en Pages : 510
Book Description
The material in this book is designed for a standard graduate course on probability theory, including some important applications. It was prepared from the sets of lecture notes for a course that I have taught several times over the past 20 years. The present version reflects the reactions of my audiences as well as some of the textbooks that I used.
Author: P. Hall
Author: P. Hall
Author: David Williams
Author: B. Ramdas Bhat
Author: James Davidson
Author: Zhengyan Lin
Author: Narahari U Prabhu
Author: 
Author: Jean Jacod
Author: Allan Gut
Author: M. M. Rao