Semimartingales and their statistical inference:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall
1999
|
| Series: | Monographs on statistics and applied probability
83 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008572738&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | 582 S. |
| ISBN: | 1584880082 9781584880080 |
Staff View
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| 245 | 1 | 0 | |a Semimartingales and their statistical inference |c B. L. S. Prakasa Rao |
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| 650 | 4 | |a Mathematical statistics |x Asymptotic theory | |
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Record in the Search Index
| DE-BY-TUM_call_number | 0048 MAT 605f 2017 A 3794 |
|---|---|
| DE-BY-TUM_katkey | 2276563 |
| DE-BY-TUM_location | LSB |
| DE-BY-TUM_media_number | 040008258015 |
| _version_ | 1821933346795552768 |
| adam_text | IMAGE 1
SEMIMARTINGALES
AND THEIR
STATISTICAL INFERENCE
B.L.S. PRAKASA RAO INDIAN STATISTICAL INSTITUTE NEW DELHI, INDIA
CHAPMAN & HALL/CRC BOCA RATEN LONDON NEW YORK WASHINGTON, D.C.
IMAGE 2
CONTENTS
PREFACE XI
1 SEMIMARTINGALES 1
1.1 INTRODUCTION 1
1.2 STOCHASTIC PROCESSES 2
MARTINGALES 11
1.3 DOOB-MEYER DECOMPOSITION 22
1.4 STOCHASTIC INTEGRATION 27
STOCHASTIC INTEGRALS WITH RESPECT TO A WIENER PROCESS 27
STOCHASTIC INTEGRATION WITH RESPECT TO A SQUARE INTEGRABLE MARTINGALE 39
QUADRATIC CHARACTERISTIC AND QUADRATIC VARIATION PROCESSES 42
CENTRAL LIMIT THEOREM 47
1.5 LOCAL MARTINGALES 49
STOCHASTIC INTEGRAL WITH RESPECT TO A LOCAL MARTINGALE . . .. 53 SOME
INEQUALITIES FOR LOCAL MARTINGALES 56
STRANG LAW OF LARGE NUMBERS 60
A MARTINGALE CONDITIONAL LAW 63
LIMIT THEOREMS FOR CONTINUOUS LOCAL MARTINGALES 65
SOME ADDITIONAL RESULTS ON STOCHASTIC INTEGRALS WITH RESPECT TO SQUARE
INTEGRABLE LOCAL MARTINGALES . . .. 68 1.6 SEMIMARTINGALES 71
STOCHASTIC INTEGRAL WITH RESPECT TO A SEMIMARTINGALE 73
PRODUCT FORMULAE FOR SEMIMARTINGALES 74
GENERALIZED ITO-VENTZELL FORMULA 75
IMAGE 3
CONTENTS
CONVERGENCE OF QUADRATIC VARIATION OF SEMIMARTINGALES 77
YOERUP S THEOREM FOR LOCAL MARTINGALES 78
STOCHASTIC DIFFERENTIAL EQUATIONS 86
RANDOM MEASURES 87
STOCHASTIC INTEGRAL WITH RESPECT TO THE MEASURE I - V . . .. 90
DECOMPOSITION OF LOCAL MARTINGALES USING STOCHASTIC INTEGRALS 92
1.7 GIRSANOV S THEOREM 97
GIRSANOV S THEOREM FOR SEMIMARTINGALES 101
GIRSANOV S THEOREM FOR SEMIMARTINGALES (MULTIDIMENSIONAL VERSION) 102
GAUSSIAN MARTINGALES 104
1.8 LIMIT THEOREMS FOR SEMIMARTINGALES 105
STAHLE CONVERGENCE OF SEMIMARTINGALES 107
1.9 DIFFUSION-TYPE PROCESSES 115
DIFFUSION PROCESSES 115
EIGEN FUNCTIONS AND MARTINGALES 119
STOCHASTIC MODELING 122
EXAMPLES OF DIFFUSION PROCESSES 123
DIFFUSION-TYPE PROCESSES 125
1.10 POINT PROCESSES 130
UNIVARIATE POINT PROCESS (SIMPLE) 130
MULTIVARIATE POINT PROCESS 137
DOUBLY STOCHASTIC POISSON PROCESS 137
STOCHASTIC TIME CHANGE 140
REFERENCES 144
2 EXPONENTIAL FAMILIES OF STOCHASTIC PROCESSES 151
2.1 INTRODUCTION 151
2.2 EXPONENTIAL FAMILIES OF SEMIMARTINGALES 154
2.3 STOCHASTIC TIME TRANSFORMATION 165
REFERENCES 169
3 ASYMPTOTIC LIKELIHOOD THEORY 171
3.1 INTRODUCTION 171
DIFFERENT TYPES OF INFORMATION AND THEIR RELATIONSHIPS 171
3.2 EXAMPLES 178
3.3 ASYMPTOTIC LIKELIHOOD THEORY FOR A CLASS OF EXPONENTIAL FAMILIES OF
SEMIMARTINGALES 185
IMAGE 4
CONTENTS
3.4 ASYMPTOTIC LIKELIHOOD THEORY FOR GENERAL PROCESSES 191
3.5 EXERCISES 196
REFERENCES 198
4 ASYMPTOTIC LIKELIHOOD THEORY FOR DIFFUSION PROCESSES WITH JUMPS 201
4.1 INTRODUCTION 201
DIFFUSIONS WITH JUMPS 201
4.2 ABSOLUTE CONTINUITY FOR MEASURES GENERATED BY DIFFUSIONS WITH JUMPS
205
4.3 SCORE VECTOR AND INFORMATION MATRIX 210
4.4 ASYMPTOTIC LIKELIHOOD THEORY FOR DIFFUSION PROCESSES WITH JUMPS 215
CONSISTENCY 215
LIMITING DISTRIBUTION 218
4.5 ASYMPTOTIC LIKELIHOOD THEORY FOR A SPECIAL CLASS OF EXPONENTIAL
FAMILIES 219
4.6 EXAMPLES 222
4.7 EXERCISES 234
REFERENCES 235
5 QUASI LIKELIHOOD AND SEMIMARTINGALES 239
5.1 QUASI LIKELIHOOD AND DISCRETE TIME PROCESSES 239
5.2 QUASI LIKELIHOOD AND CONTINUOUS TIME PROCESSES 242
5.3 QUASI LIKELIHOOD AND SPECIAL SEMIMARTINGALE 243
OPTIMALITY 246
ASYMPTOTIC PROPERTIES 252
EXISTENCE AND CONSISTENCY OF THE QUASI LIKELIHOOD ESTIMATOR 253
ASYMPTOTIC NORMALITY OF THE QUASI LIKELIHOOD ESTIMATOR 256
5.4 QUASI LIKELIHOOD AND PARTIALLY SPECIFIED COUNTING PROCESSES 257
5.5 EXAMPLES 263
5.6 EXERCISES 266
REFERENCES 268
6 LOCAL ASYMPTOTIC BEHAVIOR OF SEMIMARTINGALE EXPERIMENTS 271
6.1 LOCAL ASYMPTOTIC MIXED NORMALITY 271
REGULARITY CONDITIONS 274
IMAGE 5
CONTENTS
6.2 LOCAL ASYMPTOTIC QUADRATICITY 282
LIMITING DISTRIBUTION 289
6.3 LOCAL ASYMPTOTIC INFINITE DIVISIBILITY 293
REGULARITY CONDITIONS 295
A STOCHASTIC DOMINATED CONVERGENCE THEOREM 304
6.4 LOCAL ASYMPTOTIC NORMALITY 304
6.5 MULTIPLICATIVE MODELS 309
COUNTING PROCESSES WITH MULTIPLICATIVE INTENSITY 311
6.6 EXERCISES 322
REFERENCES 327
7 LIKELIHOOD AND ASYMPTOTIC EFFICIENCY 329
7.1 FULLY SPECIFIED LIKELIHOOD (FACTORIZABLE MODELS) 329
LOCAL ASYMPTOTIC NORMALITY 332
7.2 PARTIALLY SPECIFIED LIKELIHOOD 336
7.3 PARTIAL LIKELIHOOD AND ASYMPTOTIC EFFICIENCY 349
7.4 PARTIALLY SPECIFIED LIKELIHOOD AND ASYMPTOTIC EFFICIENCY (COUNTING
PROCESSES) 352
IMPROVEMENT OF PRELIMINARY ESTIMATORS 372
REFERENCES 379
8 INFERENCE FOR COUNTING PROCESSES 381
8.1 INTRODUCTION 381
NONHOMOGENEOUS POISSON PROCESSES 381
PROCESSES OF POISSON TYPE 384
8.2 PARAMETRIC INFERENCE 387
ESTIMATION FOR NONHOMOGENEOUS POISSON PROCESS 387
ASYMPTOTIC PROPERTIES OF AN MLE 390
LIMIT BEHAVIOR OF THE LIKELIHOOD RATIO PROCESS 391
CENTRAL LIMIT THEOREM 393
M-ESTIMATION FOR A NONHOMOGENEOUS POISSON PROCESS . . .. 402 CONSISTENCY
404
ASYMPTOTIC NORMALITY 410
8.3 SEMIPARAMETRIC INFERENCE 414
CONSISTENCY 420
ASYMPTOTIC DISTRIBUTION 422
8.4 NONPARAMETRIC INFERENCE 424
ESTIMATION BY THE KERNEL METHOD (NONHOMOGENEOUS POISSON PROCESS) 424
ESTIMATION BY THE METHOD OF SIEVES 441
ESTIMATION BY THE METHOD OF PENALTY FUNCTIONS 449
IMAGE 6
CONTENTS
ESTIMATION BY THE METHOD OF MARTINGALE ESTIMATORS 454
MAXIMUM LIKELIHOOD ESTIMATION 462
8.5 ADDITIVE-MULTIPLICATIVE HAZARD MODELS 471
REFERENCES 476
9 INFERENCE FOR SEMIMARTINGALE REGRESSION MODELS 481
9.1 ESTIMATION BY THE QUASI-LEAST-SQUARES METHOD 481
CONSISTENCY 484
ASYMPTOTIC NORMALITY 492
9.2 ESTIMATION BY THE MAXIMUM LIKELIHOOD METHOD 495
ESTIMATION OF PARAMETERS WHEN THE CHARACTERISTICS OF THE NOISE ARE KNOWN
497
ESTIMATION OF THE CHARACTERISTICS OF THE NOISE 514
9.3 ESTIMATION BY THE METHOD OF SIEVES 516
9.4 NONLINEAR SEMIMARTINGALE REGRESSION MODELS 526
REFERENCES 530
10 APPLICATIONS TO STOCHASTIC MODELING 533
10.1 INTRODUCTION 533
10.2 APPLICATIONS TO ENGINEERING AND ECONOMIC SYSTEMS 533
10.3 APPLICATION TO MODELING OF NEURON MOVEMENT IN A NERVOUS SYSTEM 538
REFERENCES 541
A DOLEANS MEASURE FOR SEMIMARTINGALES AND BURKHOLDER S INEQUALITY FOR
MARTINGALES 543
A.L DOLEANS MEASURE 543
A.2 BURKHOLDER S INEQUALITY FOR MARTINGALES 544
B INTERCHANGING STOCHASTIC INTEGRATION AND ORDINARY DIFFERENTIATION AND
FUBINI-TYPE THEOREM FOR STOCHASTIC INTEGRALS 545
B.L INTERCHANGING STOCHASTIC INTEGRATION AND ORDINARY DIFFERENTIATION
545
B.2 FUBINI-TYPE THEOREM FOR STOCHASTIC INTEGRALS 550
B.3 SUFFICIENT CONDITIONS FOR THE DIFFERENTIABILITY OF AN ITO STOCHASTIC
INTEGRAL 550
C THE FUNDAMENTAL IDENTITY OF SEQUENTIAL ANALYSIS 553
IMAGE 7
CONTENTS
D STIELTJES-LEBESGUE CALCULUS 555
D.L PRODUCT FORMULA 558
D.2 APPLICATION OF PRODUCT FORMULA 560
D.3 EXPONENTIAL FORMULA 561
E A USEFUL LEMMA 565
F CONTIGUITY 569
REFERENCES 570
G NOTES 573
INDEX 579
|
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| author | Prakasa Rao, Bhagavatula L. S. 1942- |
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| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV012620917 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:33:25Z |
| institution | BVB |
| isbn | 1584880082 9781584880080 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008572738 |
| oclc_num | 40744444 |
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| physical | 582 S. |
| publishDate | 1999 |
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| publishDateSort | 1999 |
| publisher | Chapman & Hall |
| record_format | marc |
| series | Monographs on statistics and applied probability |
| series2 | Monographs on statistics and applied probability |
| spellingShingle | Prakasa Rao, Bhagavatula L. S. 1942- Semimartingales and their statistical inference Monographs on statistics and applied probability Asymptotische analyse gtt Martingalen gtt Semimartingales (Mathematics) Statistiek gtt Stochastic analysis Statistik Mathematical statistics Asymptotic theory Semimartingales Inferenzstatistik (DE-588)4247120-5 gnd Semimartingal (DE-588)4180967-1 gnd |
| subject_GND | (DE-588)4247120-5 (DE-588)4180967-1 |
| title | Semimartingales and their statistical inference |
| title_auth | Semimartingales and their statistical inference |
| title_exact_search | Semimartingales and their statistical inference |
| title_full | Semimartingales and their statistical inference B. L. S. Prakasa Rao |
| title_fullStr | Semimartingales and their statistical inference B. L. S. Prakasa Rao |
| title_full_unstemmed | Semimartingales and their statistical inference B. L. S. Prakasa Rao |
| title_short | Semimartingales and their statistical inference |
| title_sort | semimartingales and their statistical inference |
| topic | Asymptotische analyse gtt Martingalen gtt Semimartingales (Mathematics) Statistiek gtt Stochastic analysis Statistik Mathematical statistics Asymptotic theory Semimartingales Inferenzstatistik (DE-588)4247120-5 gnd Semimartingal (DE-588)4180967-1 gnd |
| topic_facet | Asymptotische analyse Martingalen Semimartingales (Mathematics) Statistiek Stochastic analysis Statistik Mathematical statistics Asymptotic theory Semimartingales Inferenzstatistik Semimartingal |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008572738&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002494005 |
| work_keys_str_mv | AT prakasaraobhagavatulals semimartingalesandtheirstatisticalinference |
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0048 MAT 605f 2017 A 3794
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| Copy 1 | On permanent loan Ausgeliehen – Due: 31.12.9999 |