Lattice Path Counting and Applications (Probability & Mathematical Statistics Monograph)

Title page......Page 1
Contents......Page 5
PREFACE......Page 7
ACKNOWLEDGMENTS......Page 9
1. Introduction......Page 11
3. Reflection Principle (Conjugation)......Page 12
4. Method of Penetrating Analysis......Page 17
5. Recurrence and Generating Function Method......Page 20
6. Vector Representation, Compositions, and Domination......Page 24
7. Diagonal Steps......Page 29
8. Summary and Concluding Remarks......Page 31
Exercises......Page 34
References......Page 37
1. Introduction......Page 41
2. Paths within General Boundaries......Page 42
3. Some Generalizations......Page 49
4. Higher Dimensional Paths......Page 54
5. Types of Diagonal Steps and a Correspondence......Page 62
6. Concluding Remarks......Page 66
Exercises......Page 67
References......Page 70
1. Introduction......Page 73
2. Takacs' Urn Problem......Page 74
3. Chung-Feller Theorems......Page 79
4. Sparre Andersen's Equivalence......Page 87
5. Concluding Remarks......Page 90
Exercises......Page 91
References......Page 92
1. Introduction......Page 95
2. Random Walks......Page 96
3. Rank Order Statistics-Gnedenko's Technique......Page 111
4. Rank Order Statistics-- The Dwass Technique......Page 118
5. Concluding Remarks......Page 125
Exercises......Page 130
References......Page 132
1. Introduction......Page 137
2. Discrete Distributions and a Correlated Random Walk......Page 138
3. Queues......Page 149
4. Trees and Search Codes......Page 155
5. Concluding Remarks......Page 167
Exercises......Page 168
References......Page 172
1. Introduction......Page 175
2. Convolution Identities......Page 176
3. Orthogonal Relations and Inversion Formulas......Page 183
4. Concluding Remarks......Page 187
Exercises......Page 188
References......Page 190
INDEX......Page 193