Lattice Path Counting and Applications
- 1st Edition - July 10, 2014
- Imprint: Academic Press
- Author: Gopal Mohanty
- Editors: Z. W. Birnbaum, E. Lukacs
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 0 5 3 7 - 3
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 1 8 8 0 - 9
Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Lattice Path Counting and Applications focuses on the principles, methodologies, and approaches… Read more
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Request a sales quoteProbability and Mathematical Statistics: A Series of Monographs and Textbooks: Lattice Path Counting and Applications focuses on the principles, methodologies, and approaches involved in lattice path counting and applications, including vector representation, random walks, and rank order statistics. The book first underscores the simple and general boundaries of path counting. Topics include types of diagonal steps and a correspondence, paths within general boundaries, higher dimensional paths, vector representation, compositions, and domination, recurrence and generating function method, and reflection principle. The text then examines invariance and fluctuation and random walk and rank order statistics. Discussions focus on random walks, rank order statistics, Chung-Feller theorems, and Sparre Andersen's equivalence. The manuscript takes a look at convolution identities and inverse relations and discrete distributions, queues, trees, and search codes, as well as discrete distributions and a correlated random walk, trees and search codes, convolution identities, and orthogonal relations and inversion formulas. The text is a valuable reference for mathematicians and researchers interested in in lattice path counting and applications.
PrefaceAcknowledgements1. Path Counting—Simple Boundaries 1. Introduction 2. Two-Dimensional Lattice Paths 3. Reflection Principle (Conjugation) 4. Method of Penetrating Analysis 5. Recurrence and Generating Function Method 6. Vector Representation, Compositions, and Domination 7. Diagonal Steps 8. Summary and Concluding Remarks Exercises References2. Path Counting—General Boundaries 1. Introduction 2. Paths within General Boundaries 3. Some Generalizations 4. Higher Dimensional Paths 5. Types of Diagonal Steps and a Correspondence 6. Concluding Remarks Exercises References3. Invariance and Fluctuation 1. Introduction 2. Takacs' Urn Problem 3. Chung-Feller Theorems 4. Sparre Andersen's Equivalence 5. Concluding Remarks Exercises References4. Random Walk and Rank Order Statistics 1. Introduction 2. Random Walks 3. Rank Order Statistics—Gnedenko's Technique 4. Rank Order Statistics—The Dwass Technique 5. Concluding Remarks Exercises References5. Discrete Distributions, Queues, Trees, and Search Codes 1. Introduction 2. Discrete Distributions and a Correlated Random Walk 3. Queues 4. Trees and Search Codes 5. Concluding Remarks Exercises References6. Convolution Identities and Inverse Relations 1. Introduction 2. Convolution Identities 3. Orthogonal Relations and Inversion Formulas 4. Concluding Remarks Exercises ReferencesIndex
- Edition: 1
- Published: July 10, 2014
- Imprint: Academic Press
- Language: English
- Paperback ISBN: 9781483205373
- eBook ISBN: 9781483218809
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E. Lukacs
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Bowling Green State UniversityRead Lattice Path Counting and Applications on ScienceDirect