Distributions Of Intersections Returns And Positive Returns In A Generalised Random Walk
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Intersections of Random Walks
Author | : Gregory F. Lawler |
Publisher | : Springer Science & Business Media |
Total Pages | : 219 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 1475721374 |
A more accurate title for this book would be "Problems dealing with the non-intersection of paths of random walks. " These include: harmonic measure, which can be considered as a problem of nonintersection of a random walk with a fixed set; the probability that the paths of independent random walks do not intersect; and self-avoiding walks, i. e. , random walks which have no self-intersections. The prerequisite is a standard measure theoretic course in probability including martingales and Brownian motion. The first chapter develops the facts about simple random walk that will be needed. The discussion is self-contained although some previous expo sure to random walks would be helpful. Many of the results are standard, and I have made borrowed from a number of sources, especially the ex cellent book of Spitzer [65]. For the sake of simplicity I have restricted the discussion to simple random walk. Of course, many of the results hold equally well for more general walks. For example, the local central limit theorem can be proved for any random walk whose increments have mean zero and finite variance. Some of the later results, especially in Section 1. 7, have not been proved for very general classes of walks. The proofs here rely heavily on the fact that the increments of simple random walk are bounded and symmetric.
Random Walk Intersections
Author | : Xia Chen |
Publisher | : American Mathematical Soc. |
Total Pages | : 346 |
Release | : 2010 |
Genre | : Mathematics |
ISBN | : 0821848208 |
Involves important and non-trivial results in contemporary probability theory motivated by polymer models, as well as other topics of importance in physics and chemistry.
Two-Dimensional Random Walk
Author | : Serguei Popov |
Publisher | : Cambridge University Press |
Total Pages | : 224 |
Release | : 2021-03-18 |
Genre | : Mathematics |
ISBN | : 1108472451 |
A visual, intuitive introduction in the form of a tour with side-quests, using direct probabilistic insight rather than technical tools.
Intersections of Random Walks
Author | : Gregoyr Lawler |
Publisher | : Birkhäuser |
Total Pages | : 225 |
Release | : 2012-07-02 |
Genre | : Mathematics |
ISBN | : 9781461207726 |
A more accurate title for this book would be "Problems dealing with the non-intersection of paths of random walks. " These include: harmonic measure, which can be considered as a problem of nonintersection of a random walk with a fixed set; the probability that the paths of independent random walks do not intersect; and self-avoiding walks, i. e. , random walks which have no self-intersections. The prerequisite is a standard measure theoretic course in probability including martingales and Brownian motion. The first chapter develops the facts about simple random walk that will be needed. The discussion is self-contained although some previous expo sure to random walks would be helpful. Many of the results are standard, and I have made borrowed from a number of sources, especially the ex cellent book of Spitzer [65]. For the sake of simplicity I have restricted the discussion to simple random walk. Of course, many of the results hold equally well for more general walks. For example, the local central limit theorem can be proved for any random walk whose increments have mean zero and finite variance. Some of the later results, especially in Section 1. 7, have not been proved for very general classes of walks. The proofs here rely heavily on the fact that the increments of simple random walk are bounded and symmetric.
Probability Theory Subject Indexes from Mathematical Reviews
Author | : American Mathematical Society |
Publisher | : |
Total Pages | : 492 |
Release | : 1987 |
Genre | : Mathematics |
ISBN | : |
A Non-Random Walk Down Wall Street
Author | : Andrew W. Lo |
Publisher | : Princeton University Press |
Total Pages | : 449 |
Release | : 2011-11-14 |
Genre | : Business & Economics |
ISBN | : 1400829097 |
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.
Random Walks and Electric Networks
Author | : Peter G. Doyle |
Publisher | : American Mathematical Soc. |
Total Pages | : 159 |
Release | : 1984-12-31 |
Genre | : Electric network topology |
ISBN | : 1614440220 |
Probability theory, like much of mathematics, is indebted to physics as a source of problems and intuition for solving these problems. Unfortunately, the level of abstraction of current mathematics often makes it difficult for anyone but an expert to appreciate this fact. Random Walks and electric networks looks at the interplay of physics and mathematics in terms of an example—the relation between elementary electric network theory and random walks —where the mathematics involved is at the college level.