Asymptotic methods in probability and statistics with applications:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
2001
|
| Schriftenreihe: | Statistics for industry and technology
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XXIII, 549 S. 26 cm |
| ISBN: | 3764342145 0817642145 |
Internformat
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Datensatz im Suchindex
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| adam_text | IMAGE 1
ASYMPTOTIC METHODS
IN PROBABILITY AND STATISTICS WITH APPLICATIONS
N. BALAKRISHNAN LA. IBRAGIMOV V.B. NEVZOROV EDITORS
BIRKHAEUSER BOSTON * BASEL * BERLIN
IMAGE 2
CONTENTS
PREFACE CONTRIBUTORS
PART I: PROBABILITY DISTRIBUTIONS
1 POSITIVE LINNIK AND DISCRETE LINNIK DISTRIBUTIONS
GERD CHRISTOPH AND KARINA SCHREIBER
1.1 DIFFERENT KINDS OF LINNIK S DISTRIBUTIONS 3 1.2 SELF-DEOMPOSABILITY
AND DISCRETE SELF-DECOMPOSABILITY 1.3 SCALING OF POSITIVE AND DISCRETE
LINNIK LAWS 8 1.4 STRICTLY STAHLE AND DISCRETE STAHLE DISTRIBUTIONS AS
LIMIT LAWS 9
1.5 ASYMPTOTIC EXPANSIONS 11 REFERENCES 15
2 ON FINITE-DIMENSIONAL ARCHIMEDEAN COPULAS S. V. MALOV
2.1 INTRODUCTION 19
2.2 STATEMENTS OF MAIN RESULTS 22 2.3 PROOFS 25
2.4 SOME EXAMPLES 30
REFERENCES 34
PART IL CHARACTERIZATIONS OF DISTRIBUTIONS
3 CHARACTERIZATION AND STABILITY PROBLEMS FOR
FINITE QUADRATIC FORMS G. CHRISTOPH, YU. PROHOROV, AND V. ULYANOV
3.1 INTRODUCTION 39
3.2 NOTATIONS AND MAIN RESULTS 40
V
IMAGE 3
VI
3.3 AUXILIARY RESULTS 43
3.4 PROOFS OF THEOREMS 47
REFERENCES 49
4 A CHARACTERIZATION OF GAUSSIAN DISTRIBUTIONS BY SIGNS OF EVEN
CUMULANTS L. B. KLEBANOV AND G. J. SZEKELY
4.1 A CONJECTURE AND MAIN THEOREM 51 4.2 AN EXAMPLE 53
REFERENCES 53
5 ON A CLASS OF PSEUDO-ISOTROPIC DISTRIBUTIONS A. A. ZINGER
5.1 INTRODUCTION 55
5.2 THE MAIN RESULTS 56
5.3 PROOFS 58
REFERENCES 61
PART III: PROBABILITIES AND MEASURES IN HLGH-DLMENSIONAL STRUCTURES
6 TIME REVERSAL OF DIFFUSION PROCESSES IN HILBERT SPACES AND MANIFOLDS
YA. BELOPOLSKAYA
6.1 DIFFUSION IN HILBERT SPACE 65 6.1.1 DUALITY OF TIME INHOMOGENEOUS
DIFFUSION PROCESSES 69 6.2 DIFFUSION IN HILBERT MANIFOLD 72
REFERENCES 79
7 LOCALIZATION OF MARJORIZING MEASURES BETTINA BUEHLER, WENBO V. LI, AND
WERNER LINDE
7.1 INTRODUCTION 81
7.2 PARTITIONS AND WEIGHTS 83
7.3 SIMPLE PROPERTIES OF 6 $ ( T) 84
7.4 TALAGRAND S PARTITIONING SCHEME 87 7.5 MAJORIZING MEASURES 88 7.6
APPROXIMATION PROPERTIES 89 7.7 GAUSSIAN PROCESSES 93 7.8 EXAMPLES 96
REFERENCES 99
IMAGE 4
CONTENTS
VII
8 MULTIDIMENSIONAL HUNGARIAN CONSTRUCTION FOR VECTORS WITH ALMOST
GAUSSIAN SMOOTH DISTRIBUTIONS 101
F. GOETZE AND A. YU. ZAITSEV
8.1 INTRODUCTION 101
8.2 THE MAIN RESULT 106
8.3 PROOFOF THEOREM 8.2.1 112 8.4 PROOF OF THEOREMS 8.1.1-8.1.4 123
REFERENCES 131
9 ON THE EXISTENCE OF WEAK SOLUTIONS FOR STOCHASTIC DIFFERENTIAL
EQUATIONS W I TH DRIVING L 2 -VALUED MEASURES 133
V. A. LEBEDEV
9.1 BASIC PROPERTIES OF CR-FINITE L^-VALUED RANDOM MEASURES 133 9.2
FORMULATION AND PROOF OF THE MAIN RESULT 135 REFERENCES 141
10 TIGHTNESS OF STOCHASTIC FAMILIES ARISING FROM RANDOMIZATION
PROCEDURES 143
MIKHAIL LIFSHITS AND MICHEL WEBER
10.1 INTRODUCTION 143
10.2 SUFFICIENT CONDITION OF TIGHTNESS IN C[0,1] 145 10.3 CONTINUOUS
GENERALIZATION 146 10.4 AN EXAMPLE OF NON-TIGHTNESS IN C[0,1] 147 10.5
SUFFICIENT CONDITION FOR TIGHTNESS IN U [0, 1] 149 10.6 INDICATOR
FUNCTIONS 151 10.7 AN EXAMPLE OF NON-TIGHTNESS IN L P , P * [1,2) 155
REFERENCES 158
11 LONG-TIME BEHAVIOR OF MULTI-PARTICLE MARKOVIAN MODELS 161
A. D. MANITA
11.1 INTRODUCTION 161
11.2 CONVERGENCE TIME TO EQUILIBRIUM 162 11.3 MULTI-PARTICLE MARKOV
CHAINS 163 11.4 H AND S-CLASSES OF ONE-PARTICLE CHAINS 165
11.5 MINIMAL CTE FOR MULTI-PARTICLE CHAINS 167 11.6 PROOFS 168
REFERENCES 176
IMAGE 5
VIII
12 APPLICATIONS OF INFINITE-DIMENSIONAL GAUSSIAN INTEGRALS 177
A. M. NIKULIN
REFERENCES 187
13 ON MAXIMUM OF GAUSSIAN NON-CENTERED FIELDS INDEXED ON SMOOTH
MANIFOLDS 189
VLADIMIR PITERBARG AND SINISHA STAMATOVICH
13.1 INTRODUCTION 189
13.2 DEFINITIONS, AUXILIARY RESULTS, MAIN RESULTS 190 13.3 PROOFS 194
REFERENCES 203
14 TYPICAL DISTRIBUTIONS: INFINITE-DIMENSIONAL APPROACHES 205 A. V.
SUDAKOV, V. N. SUDAKOV, AND H. V. WEIZSAECKER
14.1 RESULTS 205
REFERENCES 211
PART IV: W E AK AND STRONG LIMIT THEOREMS
15 A LOCAL LIMIT THEOREM FOR STATIONARY PROCESSES
IN THE DOMAIN OF ATTRACTION OF A NORMAL DISTRIBUTION 215
JON AARONSON AND MANFRED DENKER
15.1 INTRODUCTION 215
15.2 GIBBS-MARKOV PROCESSES AND FUNCTIONALS 216 15.3 LOCAL LIMIT
THEOREMS 218 REFERENCES 223
16 ON THE MAXIMAL EXCURSION OVER INCREASING RUNS 225
ANDREI FROLOV, ALEXANDER MARTIKAINEN, AND JOSEF STEINEBACH
16.1 INTRODUCTION 225
16.2 RESULTS 230
16.3 PROOFS 232
REFERENCES 240
17 ALMOST SURE BEHAVIOUR OF PARTIAL MAXIMA SEQUENCES OF SOME M-DEPENDENT
STATIONARY SEQUENCES 243
GEORGE HAIMAN AND LHASSAN HABACH
17.1 INTRODUCTION 243
17.2 PROOFOF THEOREM 17.1.2 245 REFERENCES 249
IMAGE 6
CONTENTS
IX
18 ON A STRONG LIMIT THEOREM FOR SUMS OF INDEPENDENT
RANDOM VARIABLES 251
VALENTIN V. PETROV
18.1 INTRODUCTION AND RESULTS 251 18.2 PROOFS 253
REFERENCES 256
PART V: LARGE DEVIATION PROBABILITIES
19 DEVELOPMENT OF LINNIK S WORK IN HIS INVESTIGATION
OF THE PROBABILITIES OF LARGE DEVIATION 259
A. ALESKEVICIENE, V. STATULEVICIUS, AND K. PADVELSKIS
19.1 REMINISCENCES ON YU. V. LINNIK (V. STATULEVICIUS) 259 19.2 THEOREMS
OF LARGE DEVIATIONS OF SUMS OF RANDOM VARIABLES RELATED TO A MARKOV
CHAIN 260 19.3 NON-GAUSSIAN APPROXIMATION 272
REFERENCES 274
20 LOWER BOUNDS ON LARGE DEVIATION PROBABILITIES FOR SUMS OF INDEPENDENT
RANDOM VARIABLES 277
S. V. NAGAEV
20.1 INTRODUCTION. STATEMENT OF RESULTS 277 20.2 AUXILIARY RESULTS 283
20.3 PROOF OF THEOREM 20.1.1 286 20.4 PROOFOF THEOREM 20.1.2 291
REFERENCES 294
PART VI: EMPIRICAL PROCESSES, O R D ER STATISTICS, AND RECORDS
21 CHARACTERIZATION OF GEOMETRIE DISTRIBUTION THROUGH
WEAK RECORDS 299
FAZIL A. ALIEV
21.1 INTRODUCTION 299
21.2 CHARACTERIZATION THEOREM 300 REFERENCES 306
22 ASYMPTOTIC DISTRIBUTIONS OF STATISTICS BASED ON ORDER STATISTICS AND
RECORD VALUES AND INVARIANT CONFIDENCE INTERVALS 309
ISMIHAN G. BAIRAMOV, OMER L. GEBIZLIOGLU, AND MEHMET F. KAYA
IMAGE 7
X
22.1 INTRODUCTION 309
22.2 THE MAIN RESULTS 312
REFERENCES 319
23 RECORD VALUES IN ARCHIMEDEAN COPULA PROCESSES 321
N. BALAKRISHNAN, L. N. NEVZOROVA, AND V. B. NEVZOROV
23.1 INTRODUCTION 321
23.2 MAIN RESULTS 323
23.3 SKETCH OF PROOF 327
REFERENCES 329
24 FUNCTIONAL CLT AND LIL FOR INDUCED ORDER STATISTICS 333
YU. DAVYDOV AND V. EGOROV
24.1 INTRODUCTION 333
24.2 NOTATION 335
24.3 FUNCTIONAL CENTRAL LIMIT THEOREM 335 24.4 STRASSEN BALLS 339
24.5 LAW OF THE ITERATED LOGARITHM 343 24.6 APPLICATIONS 345
REFERENCES 347
25 NOTES ON THE K MT BROWNIAN BRIDGE APPROXIMATION TO THE UNIFORM
EMPIRICAL PROCESS 351
DAVID M. MASON
25.1 INTRODUCTION 351
25.2 PROOF OF THE KMT QUANTILE INEQUALITY 355 25.3 THE DIADIC SCHEME 360
25.4 SOME COMBINATORICS 363 REFERENCES 368
26 INTER-RECORD TIMES IN POISSON PACED F A MODELS 371
H. N. NAGARAJA AND G. HOFMANN
26.1 INTRODUCTION 371
26.2 EXACT DISTRIBUTIONS 372 26.3 ASYMPTOTIC DISTRIBUTIONS 374
REFERENCES 381
PART VIL ESTIMATION OF PARAMETERS AND HYPOTHESES TESTING
27 GOODNESS-OF-FIT TESTS FOR THE GENERALIZED ADDITIVE
RISK MODELS 385
VILIJANDAS B. BAGDONAVICIUS AND MILHAIL S. NIKULIN
27.1 INTRODUCTION 385
IMAGE 8
CONTENTS
XI
27.2 TEST FOR THE FIRST GAR MODEL BASED ON THE ESTIMATED SCORE FUNCTION
387
27.3 TESTS FOR THE SECOND GAR MODEL 391 REFERENCES 393
28 THE COMBINATION OF THE SIGN AND WILCOXON TESTS FOR SYMMETRY AND THEIR
PITMAN EFFICIENCY 395
G. BURGIO AND YA. YU. NIKITIN
28.1 INTRODUCTION 395 28.2 ASYMPTOTIC DISTRIBUTION OF THE STATISTIC G N
397
28.3 PITMAN EFFICIENCY OF THE PROPOSED STATISTIC 398 28.4 BASIC
INEQUALITY FOR THE PITMAN POWER 402 28.5 PITMAN POWER FOR G N 403
28.6 CONDITIONS OF PITMAN OPTIMALITY 404 REFERENCES 406
29 EXPONENTIAL APPROXIMATION OF STATISTICAL EXPERIMENTS 409
A. A. GUSHCHIN AND E. VALKEILA
29.1 INTRODUCTION 409
29.2 CHARACTERIZATION OF EXPONENTIAL EXPERIMENTS AND THEIR CONVERGENCE
412 29.3 APPROXIMATION BY EXPONENTIAL EXPERIMENTS 415 REFERENCES 422
30 THE ASYMPTOTIC DISTRIBUTION OF A SEQUENTIAL ESTIMATOR FOR THE
PARAMETER IN AN AR(1) MODEL WITH STABLE ERRORS 425
JOOP MIJNHEER
30.1 INTRODUCTION 425
30.2 NON-SEQUENTIAL ESTIMATION 426 30.3 SEQUENTIAL ESTIMATION 431
REFERENCES 433
31 ESTIMATION BASED ON THE EMPIRICAL CHARACTERISTIC FUNCTION 435
BRUNO REMILLARD AND RADU THEODORESCU
31.1 INTRODUCTION 435
31.2 TAILWEIGHT BEHAVIOR 436 31.3 PARAMETER ESTIMATION 438 31.4 AN
ILLUSTRATION 443
31.5 NUMERICAL RESULTS AND ESTIMATOR EFFICIENCY 446 REFERENCES 447
IMAGE 9
XII
CONTENTS
32 ASYMPTOTIC BEHAVIOR OF APPROXIMATE ENTROPY 451
ANDREW L. RUKHIN
32.1 INTRODUCTION AND SUMMARY 451 32.2 MODIFIED DEFINITION OF
APPROXIMATE ENTROPY AND COVARIANCE MATRIX FOR PREQUENCIES 453
32.3 LIMITING DISTRIBUTION OF APPROXIMATE ENTROPY 457 REFERENCES 460
PART VIII: RANDOM WALKS
33 THRESHOLD PHENOMENA IN RANDOM WALKS 465
A. V. NAGAEV
33.1 INTRODUCTION 465
33.2 THRESHOLD PHENOMENA IN THE RISK PROCESS 33.3 AUXILIARY STATEMENTS
469 33.4 ASYMPTOTIC BEHAVIOR OF THE SPITZER SERIES 33.5 THE ASYMPTOTIC
BEHAVIOR OF M_I 478 33.6 THRESHOLD PROPERTIES OF THE BOUNDARY
FUNCTIONALS 480
33.7 THE LIMITING DISTRIBUTION FOR S 481 REFERENCES 484
34 IDENTIFYING A FINITE GRAPH BY ITS RANDOM WALK 487
HEINRICH V. WEIZSAECKER
REFERENCES 490
PART IX: MISCELLANEA
35 THE COMPARISON OF THE EDGEWORTH AND
BERGSTROEM EXPANSIONS 493
VLADIMIR I. CHEBOTAREV AND ANATOLUE YA. ZOLOTUKHIN
35.1 INTRODUCTION AND RESULTS 493 35.2 PROOFOF LEMMA 35.1.1 497 35.3
PROOFOF LEMMA 35.1.2 500 35.4 PROOF OF THEOREM 35.1.1 505
REFERENCES 505
36 RECENT PROGRESS IN PROBABILISTIC NUMBER THEORY 507
JONAS KUBILIUS
468
471
36.1 RESULTS 507
IMAGE 10
CONTENTS XIII
PART X: APPLICATIONS TO FINANCE
37 ON MEAN VALUE OF PROFIT FOR OPTION HOLDER:
CASES OF A NON-CLASSICAL AND THE CLASSICAL MARKET MODELS 523
0. V. RUSAKOV
37.1 NOTATION AND STATEMENTS 523 37.2 MODELS 524
37.3 RESULTS 531
REFERENCES 533
38 ON THE PROBABILITY MODELS TO CONTROL THE INVESTOR PORTFOLIO 535
S. A. VAVILOV
38.1 INTRODUCTION 535
38.2 PORTFOLIO CONSISTING OF ZERO COUPON BONDS: THE FIRST SCHEINE 537
38.3 PORTFOLIO CONSISTING OF ARBITRARY SECURITIES: THE SECOND SCHEME 541
38.4 CONTINUOUS ANALOGUE OF THE FINITE-ORDER AUTOREGRESSION 543 38.5
CONCLUSIONS 545
REFERENCES 545
INDEX 547
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:54:34Z |
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| isbn | 3764342145 0817642145 |
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| physical | XXIII, 549 S. 26 cm |
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| record_format | marc |
| series2 | Statistics for industry and technology |
| spelling | Asymptotic methods in probability and statistics with applications N. Balakrishnan ... ed. Boston [u.a.] Birkhäuser 2001 XXIII, 549 S. 26 cm txt rdacontent n rdamedia nc rdacarrier Statistics for industry and technology Literaturangaben Distribution asymptotique (Théorie des probabilités) Teoria assintótica (inferência estatística) larpcal Asymptotic distribution (Probability theory) Asymptotische Statistik (DE-588)4203167-9 gnd rswk-swf Asymptotische Wahrscheinlichkeitsverteilung (DE-588)4519235-2 gnd rswk-swf ColetÂnea (DE-588)1071861417 Konferenzschrift 1998 Sankt Petersburg gnd-content Asymptotische Wahrscheinlichkeitsverteilung (DE-588)4519235-2 s DE-604 Asymptotische Statistik (DE-588)4203167-9 s Balakrishnan, Narayanaswamy 1956- Sonstige (DE-588)122214846 oth GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009530887&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Asymptotic methods in probability and statistics with applications Distribution asymptotique (Théorie des probabilités) Teoria assintótica (inferência estatística) larpcal Asymptotic distribution (Probability theory) Asymptotische Statistik (DE-588)4203167-9 gnd Asymptotische Wahrscheinlichkeitsverteilung (DE-588)4519235-2 gnd |
| subject_GND | (DE-588)4203167-9 (DE-588)4519235-2 (DE-588)1071861417 |
| title | Asymptotic methods in probability and statistics with applications |
| title_auth | Asymptotic methods in probability and statistics with applications |
| title_exact_search | Asymptotic methods in probability and statistics with applications |
| title_full | Asymptotic methods in probability and statistics with applications N. Balakrishnan ... ed. |
| title_fullStr | Asymptotic methods in probability and statistics with applications N. Balakrishnan ... ed. |
| title_full_unstemmed | Asymptotic methods in probability and statistics with applications N. Balakrishnan ... ed. |
| title_short | Asymptotic methods in probability and statistics with applications |
| title_sort | asymptotic methods in probability and statistics with applications |
| topic | Distribution asymptotique (Théorie des probabilités) Teoria assintótica (inferência estatística) larpcal Asymptotic distribution (Probability theory) Asymptotische Statistik (DE-588)4203167-9 gnd Asymptotische Wahrscheinlichkeitsverteilung (DE-588)4519235-2 gnd |
| topic_facet | Distribution asymptotique (Théorie des probabilités) Teoria assintótica (inferência estatística) Asymptotic distribution (Probability theory) Asymptotische Statistik Asymptotische Wahrscheinlichkeitsverteilung ColetÂnea Konferenzschrift 1998 Sankt Petersburg |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009530887&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT balakrishnannarayanaswamy asymptoticmethodsinprobabilityandstatisticswithapplications |