| Preface to the 1st edition | p. v |
| Preface to the 2nd edition | p. vii |
| Notation and Symbols | p. xiii |
| Introduction | p. 1 |
| Limit Theorems for Stopped Random Walks | p. 9 |
| Introduction | p. 9 |
| a.s. Convergence and Convergence in Probability | p. 12 |
| Anscombe's Theorem | p. 16 |
| Moment Convergence in the Strong Law and the Central Limit Theorem | p. 18 |
| Moment Inequalities | p. 21 |
| Uniform Integrability | p. 30 |
| Moment Convergence | p. 39 |
| The Stopping Summand | p. 42 |
| The Law of the Iterated Logarithm | p. 44 |
| Complete Convergence and Convergence Rates | p. 45 |
| Problems | p. 47 |
| Renewal Processes and Random Walks | p. 49 |
| Introduction | p. 49 |
| Renewal Processes; Introductory Examples | p. 50 |
| Renewal Processes; Definition and General Facts | p. 51 |
| Renewal Theorems | p. 54 |
| Limit Theorems | p. 57 |
| The Residual Lifetime | p. 61 |
| Further Results | p. 64 |
| p. 64 |
| p. 65 |
| p. 65 |
| p. 66 |
| p. 66 |
| p. 66 |
| Random Walks; Introduction and Classifications | p. 66 |
| Ladder Variables | p. 69 |
| The Maximum and the Minimum of a Random Walk | p. 71 |
| Representation Formulas for the Maximum | p. 72 |
| Limit Theorems for the Maximum | p. 74 |
| Renewal Theory for Random Walks with Positive Drift | p. 79 |
| Introduction | p. 79 |
| Ladder Variables | p. 82 |
| Finiteness of Moments | p. 83 |
| The Strong Law of Large Numbers | p. 88 |
| The Central Limit Theorem | p. 91 |
| Renewal Theorems | p. 93 |
| Uniform Integrability | p. 96 |
| Moment Convergence | p. 98 |
| Further Results on E¿(t) and Var ¿(t) | p. 100 |
| The Overshoot | p. 103 |
| The Law of the Iterated Logarithm | p. 108 |
| Complete Convergence and Convergence Rates | p. 109 |
| Applications to the Simple Random Walk | p. 109 |
| Extensions to the Non-I.I.D. Case | p. 112 |
| Problems | p. 112 |
| Generalizations and Extensions | p. 115 |
| Introduction | p. 115 |
| A Stopped Two-Dimensional Random Walk | p. 116 |
| Some Applications | p. 126 |
| Chromatographic Methods | p. 126 |
| Motion of Water in a River | p. 129 |
| The Alternating Renewal Process | p. 129 |
| Cryptomachines | p. 130 |
| Age Replacement Policies | p. 130 |
| Age Replacement Policies; Cost Considerations | p. 132 |
| Random Replacement Policies | p. 132 |
| Counter Models | p. 132 |
| Insurance Risk Theory | p. 133 |
| The Queueing System M/G/1 | p. 134 |
| The Waiting Time in a Roulette Game | p. 134 |
| A Curious (?) Problem | p. 136 |
| The Maximum of a Random Walk with Positive Drift | p. 136 |
| First Passage Times Across General Boundaries | p. 141 |
| Functional Limit Theorems | p. 157 |
| Introduction | p. 157 |
| An Anscombe–Donsker Invariance Principle | p. 157 |
| First Passage Times for Random Walks with Positive Drift | p. 162 |
| A Stopped Two-Dimensional Random Walk | p. 167 |
| The Maximum of a Random Walk with Positive Drift | p. 169 |
| First Passage Times Across General Boundaries | p. 170 |
| The Law of the Iterated Logarithm | p. 172 |
| Further Results | p. 174 |
| Perturbed Random Walks | p. 175 |
| Introduction | p. 175 |
| Limit Theorems; the General Case | p. 178 |
| Limit Theorems; the Case <$>Z_n = n cdot g(bar Y_n)<$> | p. 183 |
| Convergence Rates | p. 190 |
| Finiteness of Moments; the General Case | p. 190 |
| Finiteness of Moments; the Case <$>Z_n = n cdot g (bar Y_n)<$> | p. 194 |
| Moment Convergence; the General Case | p. 198 |
| Moment Convergence; the Case <$>Z_n = n cdot g(bar Y_n)<$> | p. 200 |
| Examples | p. 202 |
| Stopped Two-Dimensional Perturbed Random Walks | p. 205 |
| The Case <$>Z_n = n cdot g(bar Y_n)<$> | p. 209 |
| An Application | p. 211 |
| Remarks on Further Results and Extensions | p. 214 |
| Problems | p. 221 |
| Some Facts from Probability Theory | p. 223 |
| Convergence of Moments. Uniform Integrability | p. 223 |
| Moment Inequalities for Martingales | p. 225 |
| Convergence of Probability Measures | p. 229 |
| Strong Invariance Principles | p. 234 |
| Problems | p. 235 |
| Some Facts about Regularly Varying Functions | p. 237 |
| Introduction and Definitions | p. 237 |
| Some Results | p. 238 |
| References | p. 241 |
| Index | p. 257 |
| Table of Contents provided by Ingram. All Rights Reserved. |
