Large deviations and idempotent probability:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall
2001
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| Series: | Chapman & Hall/CRC monographs and surveys in pure and applied mathematics
119 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 500 S. |
| ISBN: | 1584881984 |
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Record in the Search Index
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| adam_text | N CHAPMAN & HALL/CRC MONOGRAPHS AND SURVEYS IN PURE AND APPLIED
MATHEMATICS I 19 LARGE DEVIATIONS AND IDEMPOTENT PROBABILITY ANATOLII
PUHALSKII CHAPMAN & HALL/CRC BOCA RATON LONDON NEW YORK WASHINGTON, D.C.
CONTENTS PREFACE XI BASIC NOTATION 1 I IDEMPOTENT PROBABILITY THEORY 3 1
IDEMPOTENT PROBABILITY MEASURES 5 1.1 IDEMPOTENT MEASURES 5 1.2
MEASURABLE FUNCTIONS 14 1.3 MODES OF CONVERGENCE 17 1.4 IDEMPOTENT
INTEGRATION 20 1.5 PRODUCT SPACES 32 1.6 INDEPENDENCE AND CONDITIONING
36 1.7 IDEMPOTENT MEASURES ON TOPOLOGICAL SPACES 51 1.8 IDEMPOTENT
MEASURES ON PROJECTIVE LIMITS 58 1.9 TOPOLOGICAL SPACES OF IDEMPOTENT
PROBABILITIES 64 1.10 DERIVED WEAK CONVERGENCE 79 1.11 LAPLACE-FENCHEL
TRANSFORM . 84 2 MAXINGALES 91 2.1 IDEMPOTENT STOPPING TIMES 91 2.2
IDEMPOTENT PROCESSES 95 2.3 EXPONENTIAL MAXINGALES 104 2.4 WIENER AND
POISSON IDEMPOTENT PROCESSES 114 2.5 IDEMPOTENT STOCHASTIC INTEGRALS 124
2.6 IDEMPOTENT ITO DIFFERENTIAL EQUATIONS 151 VN VLLL 2.7 SEMIMAXINGALES
170 2.8 MAXINGALE PROBLEMS 202 II LARGE DEVIATION CONVERGENCE OF
SEMIMARTINGALES 251 3 LARGE DEVIATION CONVERGENCE 253 3.1 LARGE
DEVIATION CONVERGENCE IN TIHONOV SPACES . . . . 253 3.2 LARGE DEVIATION
CONVERGENCE IN THE SKOROHOD SPACE 276 4 THE METHOD OF FINITE-DIMENSIONAL
DISTRIBUTIONS 289 4.1 CONVERGENCE OF STOCHASTIC EXPONENTIALS 290 4.2
CONVERGENCE OF CHARACTERISTICS 305 4.2.1 THE CASE OF SMALL JUMPS 316
4.2.2 THE GENERAL CASE 325 4.3 COROLLARIES 332 4.4 APPLICATIONS TO
PARTIAL-SUM PROCESSES 342 5 THE METHOD OF THE MAXINGALE PROBLEM 355 5.1
CONVERGENCE OF STOCHASTIC EXPONENTIALS 356 5.1.1 PROOFS 360 5.2
CONVERGENCE OF CHARACTERISTICS 373 5.2.1 EXPONENTIAL TIGHTNESS RESULTS
380 5.2.2 LD ACCUMULATION POINTS AS SOLUTIONS TO MAXIN- GALE PROBLEMS
391 5.2.3 PROOFS OF THE MAIN RESULTS 404 5.3 LARGE DEVIATION CONVERGENCE
RESULTS 406 5.4 LARGE DEVIATION CONVERGENCE OF MARKOV PROCESSES . . .
414 6 LARGE DEVIATION CONVERGENCE OF QUEUEING PROCESSES 433 6.1 MODERATE
DEVIATIONS IN QUEUEING NETWORKS 433 6.1.1 IDEMPOTENT DIFFUSION
APPROXIMATION FOR SINGLE SERVER QUEUES 433 6.1.2 IDEMPOTENT DIFFUSION
APPROXIMATION FOR QUEUEING NETWORKS 442 6.2 VERY LARGE AND MODERATE
DEVIATIONS FOR MANY SERVER QUEUES 450 IX APPENDIX A AUXILIARY LEMMAS 457
APPENDIX B NOTES AND REMARKS 467 BIBLIOGRAPHY 483 INDEX 495
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| spellingShingle | Puchalskij, Anatolij Large deviations and idempotent probability Chapman & Hall/CRC monographs and surveys in pure and applied mathematics Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd Große Abweichung (DE-588)4330658-5 gnd |
| subject_GND | (DE-588)4137556-7 (DE-588)4330658-5 |
| title | Large deviations and idempotent probability |
| title_auth | Large deviations and idempotent probability |
| title_exact_search | Large deviations and idempotent probability |
| title_full | Large deviations and idempotent probability Anatolii Puhalskii |
| title_fullStr | Large deviations and idempotent probability Anatolii Puhalskii |
| title_full_unstemmed | Large deviations and idempotent probability Anatolii Puhalskii |
| title_short | Large deviations and idempotent probability |
| title_sort | large deviations and idempotent probability |
| topic | Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd Große Abweichung (DE-588)4330658-5 gnd |
| topic_facet | Wahrscheinlichkeitsmaß Große Abweichung |
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