Download or read book Random Walk In Random And Non random Environments Second Edition written by Pal Revesz and published by World Scientific. This book was released on 2005-08-11 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Random Walk In Random And Non random Environments Third Edition written by Pal Revesz and published by World Scientific. This book was released on 2013-03-06 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 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.
Download or read book Random Walk In Random And Non random Environments written by Pal Revesz and published by World Scientific. This book was released on 1990-09-28 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Problems In Probability 2nd Edition written by Terry M Mills and published by World Scientific Publishing Company. This book was released on 2013-10-22 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Modern Approach to Probability Theory written by Bert E. Fristedt and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Non Random Walk Down Wall Street written by Andrew W. Lo and published by Princeton University Press. This book was released on 2011-11-14 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Problems in Probability written by T M Mills and published by World Scientific Publishing Company. This book was released on 2001-11-19 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Probability Theory written by Achim Klenke and published by Springer Science & Business Media. This book was released on 2013-08-30 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Brownian Motion written by René L. Schilling and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-06-18 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Primer for Unit Root Testing written by K. Patterson and published by Springer. This book was released on 2010-03-31 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Problems in Probability written by T. M. Mills and published by World Scientific. This book was released on 2001 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Asymptotic Laws and Methods in Stochastics written by Donald Dawson and published by Springer. This book was released on 2015-11-12 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains articles arising from a conference in honour of mathematician-statistician Miklόs Csörgő on the occasion of his 80th birthday, held in Ottawa in July 2012. It comprises research papers and overview articles, which provide a substantial glimpse of the history and state-of-the-art of the field of asymptotic methods in probability and statistics, written by leading experts. The volume consists of twenty articles on topics on limit theorems for self-normalized processes, planar processes, the central limit theorem and laws of large numbers, change-point problems, short and long range dependent time series, applied probability and stochastic processes, and the theory and methods of statistics. It also includes Csörgő’s list of publications during more than 50 years, since 1962.
Download or read book Non homogeneous Random Walks written by Mikhail Menshikov and published by Cambridge University Press. This book was released on 2016-12-22 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic systems provide powerful abstract models for a variety of important real-life applications: for example, power supply, traffic flow, data transmission. They (and the real systems they model) are often subject to phase transitions, behaving in one way when a parameter is below a certain critical value, then switching behaviour as soon as that critical value is reached. In a real system, we do not necessarily have control over all the parameter values, so it is important to know how to find critical points and to understand system behaviour near these points. This book is a modern presentation of the 'semimartingale' or 'Lyapunov function' method applied to near-critical stochastic systems, exemplified by non-homogeneous random walks. Applications treat near-critical stochastic systems and range across modern probability theory from stochastic billiards models to interacting particle systems. Spatially non-homogeneous random walks are explored in depth, as they provide prototypical near-critical systems.
Download or read book Stochastic Processes written by Andrei N Borodin and published by Birkhäuser. This book was released on 2017-10-30 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a rigorous yet accessible introduction to the theory of stochastic processes. A significant part of the book is devoted to the classic theory of stochastic processes. In turn, it also presents proofs of well-known results, sometimes together with new approaches. Moreover, the book explores topics not previously covered elsewhere, such as distributions of functionals of diffusions stopped at different random times, the Brownian local time, diffusions with jumps, and an invariance principle for random walks and local times. Supported by carefully selected material, the book showcases a wealth of examples that demonstrate how to solve concrete problems by applying theoretical results. It addresses a broad range of applications, focusing on concrete computational techniques rather than on abstract theory. The content presented here is largely self-contained, making it suitable for researchers and graduate students alike.
Download or read book Discrete Time Branching Processes in Random Environment written by Götz Kersting and published by John Wiley & Sons. This book was released on 2017-11-01 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Branching processes are stochastic processes which represent the reproduction of particles, such as individuals within a population, and thereby model demographic stochasticity. In branching processes in random environment (BPREs), additional environmental stochasticity is incorporated, meaning that the conditions of reproduction may vary in a random fashion from one generation to the next. This book offers an introduction to the basics of BPREs and then presents the cases of critical and subcritical processes in detail, the latter dividing into weakly, intermediate, and strongly subcritical regimes.
Download or read book Probability Theory written by Werner Linde and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-06-04 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as an introduction to Probability Theory and Mathematical Statistics for students in mathematics, the physical sciences, engineering, and related fields. It is based on the author’s 25 years of experience teaching probability and is squarely aimed at helping students overcome common difficulties in learning the subject. The focus of the book is an explanation of the theory, mainly by the use of many examples. Whenever possible, proofs of stated results are provided. All sections conclude with a short list of problems. The book also includes several optional sections on more advanced topics. This textbook would be ideal for use in a first course in Probability Theory. Contents: Probabilities Conditional Probabilities and Independence Random Variables and Their Distribution Operations on Random Variables Expected Value, Variance, and Covariance Normally Distributed Random Vectors Limit Theorems Introduction to Stochastic Processes Mathematical Statistics Appendix Bibliography Index
Download or read book Automata Languages and Programming written by Jiri Wiedermann and published by Springer. This book was released on 2003-07-31 with total page 726 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 26th International Colloquium on Automata, Languages and Programming, ICALP'99, held in Prague, Czech Republic, in July 1999. The 56 revised full papers presented were carefully reviewed and selected from a total of 126 submissions; also included are 11 inivited contributions. Among the topics addressed are approximation algorithms, algebra and circuits, concurrency, semantics and rewriting, process algebras, graphs, distributed computing, logic of programs, sorting and searching, automata, nonstandard computing, regular languages, combinatorial optimization, automata and logics, string algorithms, and applied logics.
