Random Walk In Random And Non-random Environments (Second Edition) PDF Download

Author: Pal Revesz
Publisher: World Scientific
ISBN: 9814480223
Category : Mathematics
Languages : en
Pages : 397

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Book Description
The simplest mathematical model of the Brownian motion of physics is the simple, symmetric random walk. This book collects and compares current results — mostly strong theorems which describe the properties of a random walk. The modern problems of the limit theorems of probability theory are treated in the simple case of coin tossing. Taking advantage of this simplicity, the reader is familiarized with limit theorems (especially strong ones) without the burden of technical tools and difficulties. An easy way of considering the Wiener process is also given, through the study of the random walk.Since the first edition was published in 1990, a number of new results have appeared in the literature. The original edition contained many unsolved problems and conjectures which have since been settled; this second revised and enlarged edition includes those new results. Three new chapters have been added: frequently and rarely visited points, heavy points and long excursions. This new edition presents the most complete study of, and the most elementary way to study, the path properties of the Brownian motion.

Author: P l R‚v‚sz
Publisher: World Scientific
ISBN: 981444751X
Category : Mathematics
Languages : en
Pages : 421

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Book Description
The simplest mathematical model of the Brownian motion of physics is the simple, symmetric random walk. This book collects and compares current results OCo mostly strong theorems which describe the properties of a random walk. The modern problems of the limit theorems of probability theory are treated in the simple case of coin tossing. Taking advantage of this simplicity, the reader is familiarized with limit theorems (especially strong ones) without the burden of technical tools and difficulties. An easy way of considering the Wiener process is also given, through the study of the random walk.Since the first and second editions were published in 1990 and 2005, a number of new results have appeared in the literature. The first two editions contained many unsolved problems and conjectures which have since been settled; this third, revised and enlarged edition includes those new results. In this edition, a completely new part is included concerning Simple Random Walks on Graphs. Properties of random walks on several concrete graphs have been studied in the last decade. Some of the obtained results are also presented.

Author: Pal Revesz
Publisher: World Scientific
ISBN: 9814551899
Category :
Languages : en
Pages : 348

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Book Description
This book collects and compares the results — mostly strong theorems which describe the properties of a simple symmetric random walk. The newest problems of limit theorems of probability theory are treated in the very simple case of coin tossing. Using the advantage of this simple situation, the reader can become familiar with limit theorems (especially strong ones) without suffering from technical tools and difficulties. A simple way to the study of the Wiener process is also given, through the study of the random walk. This book presents the most complete study of, and the most elementary way to the study of, the path properties of the Wiener process; and the most elementary way to the study of the strong theorems of probability theory.

Author: Terry M Mills
Publisher: World Scientific Publishing Company
ISBN: 9814551473
Category : Mathematics
Languages : en
Pages : 192

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Book Description
This is a book of problems in probability and their solutions. The work has been written for undergraduate students who have a background in calculus and wish to study probability.Probability theory is a key part of contemporary mathematics. The subject plays a key role in the insurance industry, modelling financial markets, and statistics in general — including all those fields of endeavour to which statistics is applied (e.g. health, physical sciences, engineering, economics, social sciences). Every student majoring in mathematics at university ought to take a course on probability or mathematical statistics. Probability is now a standard part of high school mathematics, and teachers ought to be well versed and confident in the subject. Problem solving is important in mathematics. This book combines problem solving and probability.

Author: Bert E. Fristedt
Publisher: Springer Science & Business Media
ISBN: 1489928375
Category : Mathematics
Languages : en
Pages : 775

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Book Description
Students and teachers of mathematics and related fields will find this book a comprehensive and modern approach to probability theory, providing the background and techniques to go from the beginning graduate level to the point of specialization in research areas of current interest. The book is designed for a two- or three-semester course, assuming only courses in undergraduate real analysis or rigorous advanced calculus, and some elementary linear algebra. A variety of applications—Bayesian statistics, financial mathematics, information theory, tomography, and signal processing—appear as threads to both enhance the understanding of the relevant mathematics and motivate students whose main interests are outside of pure areas.

Author: T M Mills
Publisher: World Scientific Publishing Company
ISBN: 9813105836
Category :
Languages : en
Pages : 192

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Book Description
Probability theory is an important part of contemporary mathematics. It plays a key role in the insurance industry, in the modelling of financial markets, and in statistics generally — including all those fields of endeavour to which statistics is applied (e.g. health, physical sciences, engineering, economics). The 20th century has been an important period for the subject, because we have witnessed the development of a solid mathematical basis for the study of probability, especially from the Russian school of probability under the leadership of A N Kolmogorov. We have also seen many new applications of probability — from applications of stochastic calculus in the financial industry to Internet gambling. At the beginning of the 21st century, the subject offers plenty of scope for theoretical developments, modern applications and computational problems. There is something for everyone in probability! The notes and problems in this book have been designed to provide a basis for a series of lectures suitable for advanced undergraduate students on the subject of probability. Through problem solving, students can experience the excitement associated with probability. This activity will help them to develop their problem-solving skills, which are so valuable in today's world. The problems in the book will introduce the student to some famous works and workers in probability and convey the historical, classical and contemporary aspects of probability. A key feature of the book is that many problems are in fact small guided research projects. The research work involved in solving the problems will enhance the student's library research skills.

Author: Andrew W. Lo
Publisher: Princeton University Press
ISBN: 1400829097
Category : Business & Economics
Languages : en
Pages : 449

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Book Description
For over half a century, financial experts have regarded the movements of markets as a random walk--unpredictable meanderings akin to a drunkard's unsteady gait--and this hypothesis has become a cornerstone of modern financial economics and many investment strategies. Here Andrew W. Lo and A. Craig MacKinlay put the Random Walk Hypothesis to the test. In this volume, which elegantly integrates their most important articles, Lo and MacKinlay find that markets are not completely random after all, and that predictable components do exist in recent stock and bond returns. Their book provides a state-of-the-art account of the techniques for detecting predictabilities and evaluating their statistical and economic significance, and offers a tantalizing glimpse into the financial technologies of the future. The articles track the exciting course of Lo and MacKinlay's research on the predictability of stock prices from their early work on rejecting random walks in short-horizon returns to their analysis of long-term memory in stock market prices. A particular highlight is their now-famous inquiry into the pitfalls of "data-snooping biases" that have arisen from the widespread use of the same historical databases for discovering anomalies and developing seemingly profitable investment strategies. This book invites scholars to reconsider the Random Walk Hypothesis, and, by carefully documenting the presence of predictable components in the stock market, also directs investment professionals toward superior long-term investment returns through disciplined active investment management.

Author: Achim Klenke
Publisher: Springer Science & Business Media
ISBN: 1447153618
Category : Mathematics
Languages : en
Pages : 633

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Book Description
This second edition of the popular textbook contains a comprehensive course in modern probability theory, covering a wide variety of topics which are not usually found in introductory textbooks, including: • limit theorems for sums of random variables • martingales • percolation • Markov chains and electrical networks • construction of stochastic processes • Poisson point process and infinite divisibility • large deviation principles and statistical physics • Brownian motion • stochastic integral and stochastic differential equations. The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts in probability theory. This second edition has been carefully extended and includes many new features. It contains updated figures (over 50), computer simulations and some difficult proofs have been made more accessible. A wealth of examples and more than 270 exercises as well as biographic details of key mathematicians support and enliven the presentation. It will be of use to students and researchers in mathematics and statistics in physics, computer science, economics and biology.

Author: René L. Schilling
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110307308
Category : Mathematics
Languages : en
Pages : 424

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Book Description
Brownian motion is one of the most important stochastic processes in continuous time and with continuous state space. Within the realm of stochastic processes, Brownian motion is at the intersection of Gaussian processes, martingales, Markov processes, diffusions and random fractals, and it has influenced the study of these topics. Its central position within mathematics is matched by numerous applications in science, engineering and mathematical finance. Often textbooks on probability theory cover, if at all, Brownian motion only briefly. On the other hand, there is a considerable gap to more specialized texts on Brownian motion which is not so easy to overcome for the novice. The authors’ aim was to write a book which can be used as an introduction to Brownian motion and stochastic calculus, and as a first course in continuous-time and continuous-state Markov processes. They also wanted to have a text which would be both a readily accessible mathematical back-up for contemporary applications (such as mathematical finance) and a foundation to get easy access to advanced monographs. This textbook, tailored to the needs of graduate and advanced undergraduate students, covers Brownian motion, starting from its elementary properties, certain distributional aspects, path properties, and leading to stochastic calculus based on Brownian motion. It also includes numerical recipes for the simulation of Brownian motion.

Author: K. Patterson
Publisher: Springer
ISBN: 0230248454
Category : Business & Economics
Languages : en
Pages : 301

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Book Description
This book gives an authoritative overview of the literature on non-stationarity, integration and unit roots, providing direction and guidance. It also provides detailed examples to show how the techniques can be applied in practical situations and the pitfalls to avoid.