Probability theory with applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Springer
2006
|
| Edition: | 2. ed. |
| Series: | Mathematics and its applications
|
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014738090&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Literatur-Verz.: S. 509 - 517 |
| Physical Description: | XVIII, 527 S. graph. Darst. |
| ISBN: | 0387277307 9780387277301 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1819327642754613248 |
|---|---|
| adam_text | PROBABILITY THEORY WITH APPLICATIONS SECOND EDITION BY M.M. RAO
UNIVERSITY OF CALIFORNIA, RIVERSIDE, CALIFORNIA RJ. SWIFT CALIFORNIA
STATE POLYTECHNIC UNIVERSITY, POMONA, CALIFORNIA ^J SPRINGER CONTENTS
PREFACE TO SECOND EDITION IX PREFACE TO FIRST EDITION XV LIST OF SYMBOLS
XVII PART I - FOUNDATIONS 1 1 BACKGROUND MATERIAL AND PRELIMINARIES 3
1.1 WHAT IS PROBABILITY? 3 1.2 RANDOM VARIABLES AND MEASURABILITY
RESULTS 7 1.3 EXPECTATIONS AND THE LEBESGUE THEORY 12 1.4 IMAGE MEASURE
AND THE FUNDAMENTAL THEOREM OF PROBABILITY . 20 EXERCISES 28 2
INDEPENDENCE AND STRONG CONVERGENCE 33 2.1 INDEPENDENCE 33 2.2
CONVERGENCE CONCEPTS, SERIES AND INEQUALITIES 46 2.3 LAWS OF LARGE
NUMBERS 58 2.4 APPLICATIONS TO EMPIRIC DISTRIBUTIONS, DENSITIES,
QUEUEING, AND RANDOM WALK 68 EXERCISES . . 87 3 CONDITIONING AND SOME
DEPENDENCE CLASSES 103 3.1 CONDITIONAL EXPECTATIONS 103 3.2 CONDITIONAL
PROBABILITIES 120 3.3 MARKOV DEPENDENCE 140 3.4 EXISTENCE OF VARIOUS
RANDOM FAMILIES 158 3.5 MARTINGALE SEQUENCES 174 EXERCISES ? * 203 PART
II - ANALYTICAL THEORY 221 4 PROBABILITY DISTRIBUTIONS AND
CHARACTERISTIC FUNCTIONS .... 223 4.1 DISTRIBUTION FUNCTIONS AND THE
SELECTION PRINCIPLE 223 4.2 CHARACTERISTIC FUNCTIONS, INVERSION, AND
LEVY S CONTINUITY THEOREM 234 4.3 CRAMER S THEOREM ON FOURIER TRANSFORMS
OF SIGNED MEASURES . 251 4.4 BOCHNER S THEOREM ON POSITIVE DEFINITE
FUNCTIONS 256 VIII CONTENTS 4.5 SOME MULTIDIMENSIONAL EXTENSIONS 265 4.6
EQUIVALENCE OF CONVERGENCES FOR SUMS OF INDEPENDENT RANDOM VARIABLES 274
EXERCISES 276 5 WEAK LIMIT LAWS 291 5.1 CLASSICAL CENTRAL LIMIT THEOREMS
291 5.2 INFINITE DIVISIBILITY AND THE LEVY-KHINTCHINE FORMULA 304 5.3
GENERAL LIMIT LAWS, INCLUDING STABILITY 318 5.4 INVARIANCE PRINCIPLE 341
5.5 KOLMOGOROV S LAW OF THE ITERATED LOGARITHM 364 5.6 APPLICATION TO A
STOCHASTIC DIFFERENCE EQUATION 375 EXERCISES 386 PART III - APPLICATIONS
409 6 STOPPING TIMES, MARTINGALES, AND CONVERGENCES 411 6.1 STOPPING
TIMES AND THEIR CALCULUS 411 6.2 WALD S EQUATION AND AN APPLICATION 415
6.3 STOPPED MARTINGALES 420 EXERCISES 427 7 LIMIT LAWS FOR SOME
DEPENDENT SEQUENCES 429 7.1 CENTRAL LIMIT THEOREMS 429 7.2 LIMIT LAWS
FOR A RANDOM NUMBER OF RANDOM VARIABLES 436 7.3 ERGODIC SEQUENCES 449
EXERCISES 455 8 A GLIMPSE OF STOCHASTIC PROCESSES 459 8.1 BROWNIAN
MOTION: DEFINITION AND CONSTRUCTION 459 8.2 SOME PROPERTIES OF BROWNIAN
MOTION 463 8.3 LAW OF THE ITERATED LOGARITHM FOR BROWNIAN MOTION 467 8.4
GAUSSIAN AND GENERAL ADDITIVE PROCESSES : 470 8.5 SECOND-ORDER PROCESSES
493 EXERCISES 498 REFERENCES 509 AUTHOR INDEX 519 SUBJECT INDEX 523
|
| any_adam_object | 1 |
| author | Rao, Malempati M. 1929- |
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| bvnumber | BV021521594 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 170 SK 800 |
| ctrlnum | (OCoLC)70911903 (DE-599)BVBBV021521594 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV021521594 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T12:35:34Z |
| institution | BVB |
| isbn | 0387277307 9780387277301 |
| language | English |
| lccn | 2005049973 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014738090 |
| oclc_num | 70911903 |
| open_access_boolean | |
| owner | DE-898 DE-BY-UBR DE-573 DE-83 |
| owner_facet | DE-898 DE-BY-UBR DE-573 DE-83 |
| physical | XVIII, 527 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Springer |
| record_format | marc |
| series2 | Mathematics and its applications |
| spellingShingle | Rao, Malempati M. 1929- Probability theory with applications Probabilities Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Stochastik (DE-588)4121729-9 gnd |
| subject_GND | (DE-588)4064324-4 (DE-588)4121729-9 |
| title | Probability theory with applications |
| title_auth | Probability theory with applications |
| title_exact_search | Probability theory with applications |
| title_full | Probability theory with applications by M. M. Rao ; R. J. Swift |
| title_fullStr | Probability theory with applications by M. M. Rao ; R. J. Swift |
| title_full_unstemmed | Probability theory with applications by M. M. Rao ; R. J. Swift |
| title_short | Probability theory with applications |
| title_sort | probability theory with applications |
| topic | Probabilities Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Stochastik (DE-588)4121729-9 gnd |
| topic_facet | Probabilities Wahrscheinlichkeitsrechnung Stochastik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014738090&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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