Mohanty / Birnbaum / Lukacs Lattice Path Counting and Applications

1. Auflage 2014
ISBN: 978-1-4832-1880-9
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 200 Seiten, Web PDF

Probability 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.

Autoren/Hrsg.

Mohanty, Gopal

Birnbaum, Z. W.

Lukacs, E.

Inhaltsverzeichnis

1;Front Cover;1
2;Lattice Path Counting and Applications;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;Preface;10
7;Acknowledgments;12
8;Chapter 1. Path Counting—Simple Boundaries;14
8.1;1. Introduction;14
8.2;2. Two-Dimensional Lattice Paths;15
8.3;3. Reflection Principle (Conjugation);15
8.4;4. Method of Penetrating Analysis;20
8.5;5. Recurrence and Generating Function Method;23
8.6;6. Vector Representation, Compositions, and Domination;27
8.7;7. Diagonal Steps;32
8.8;8. Summary and Concluding Remarks;34
8.9;Exercises;37
8.10;References;40
9;Chapter 2. Path Counting—General Boundaries ;44
9.1;1. Introduction;44
9.2;2. Paths within General Boundaries;45
9.3;3. Some Generalizations;52
9.4;4. Higher Dimensional Paths;57
9.5;5. Types of Diagonal Steps and a Correspondence;65
9.6;6. Concluding Remarks;69
9.7;Exercises;70
9.8;References;73
10;Chapter 3. Invariance and Fluctuation;76
10.1;1. Introduction;76
10.2;2. Takács' Urn Problem;77
10.3;3. Chung-Feller Theorems;82
10.4;4. Sparre Andersen's Equivalence;90
10.5;5. Concluding Remarks;93
10.6;Exercises;94
10.7;References;95
11;Chapter 4. Random Walk and Rank Order Statistics;98
11.1;1. Introduction;98
11.2;2. Random Walks;99
11.3;3. Rank Order Statistics—Gnedenko's Technique;114
11.4;4. Rank Order Statistics—The Dwass Technique;121
11.5;5. Concluding Remarks;128
11.6;Exercises;133
11.7;References;135
12;Chapter 5. Discrete Distributions, Queues, Trees, and Search Codes;140
12.1;1. Introduction;140
12.2;2. Discrete Distributions and a Correlated Random Walk;141
12.3;3. Queues;152
12.4;4. Trees and Search Codes;158
12.5;5. Concluding Remarks;170
12.6;Exercises;171
12.7;References;175
13;Chapter 6. Convolution Identities and Inverse Relations;178
13.1;1. Introduction;178
13.2;2. Convolution Identities;179
13.3;3. Orthogonal Relations and Inversion Formulas;186
13.4;4. Concluding Remarks;190
13.5;Exercises;191
13.6;References;193
14;Index;196
15;Probability and Mathematical Statistics;199