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Preface | ||
List of Figures | ||
1 | Weak convergence of stochastic processes | 1 |
1.1 | Introductory remarks | 2 |
1.2 | Weak convergence in R[subscript m] | 10 |
1.3 | Weak convergence in metric spaces | 14 |
1.4 | The space D of cadlag functions | 21 |
1.5 | J-continuous functionals | 32 |
1.6 | J-convergence of cadlag processes | 40 |
2 | Weak convergence of randomly stopped stochastic processes | 63 |
2.1 | Introductory remarks | 64 |
2.2 | Randomly stopped scalar cadlag processes | 73 |
2.3 | Randomly stopped vector cadlag processes | 77 |
2.4 | Weakened continuity conditions | 88 |
2.5 | Iterated weak limits | 107 |
2.6 | Scalar compositions of cadlag processes | 112 |
2.7 | Vector compositions of cadlag processes | 122 |
2.8 | Translation theorems | 130 |
2.9 | Randomly stopped locally compact cadlag processes | 139 |
3 | J-convergence of compositions of stochastic processes | 147 |
3.1 | Introductory remarks | 148 |
3.2 | Compositions with asymptotically continuous components | 158 |
3.3 | Asymptotically continuous external processes | 165 |
3.4 | Asymptotically continuous internal stopping processes | 173 |
3.5 | Semi-vector compositions of cadlag functions | 181 |
3.6 | Semi-vector compositions of cadlag processes | 189 |
3.7 | Vector compositions of cadlag functions | 200 |
3.8 | Vector compositions of cadlag processes | 214 |
4 | Summary of applications | 229 |
4.1 | Introductory remarks | 231 |
4.2 | Randomly stopped sum-processes | 240 |
4.3 | Generalised exceeding processes | 251 |
4.4 | Step generalised exceeding processes | 271 |
4.5 | Sum-processes with renewal stopping | 280 |
4.6 | Accumulation processes | 292 |
4.7 | Extremes with random sample size | 303 |
4.8 | Mixed sum-max processes | 310 |
4.9 | Max-processes with renewal stopping | 322 |
4.10 | Shock processes | 329 |
Bibliographical remarks | 339 | |
References | 351 | |
Index | 393 |
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Add Limit Theorems for Randomly Stopped Stochastic Processes, This volume is the first to present a state-of-the-art overview of this field, with many results published for the first time. It covers the general conditions as well as the basic applications of the theory, and it covers and demystifies the vast and tec, Limit Theorems for Randomly Stopped Stochastic Processes to the inventory that you are selling on WonderClubX
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Add Limit Theorems for Randomly Stopped Stochastic Processes, This volume is the first to present a state-of-the-art overview of this field, with many results published for the first time. It covers the general conditions as well as the basic applications of the theory, and it covers and demystifies the vast and tec, Limit Theorems for Randomly Stopped Stochastic Processes to your collection on WonderClub |