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Bibliographic Details
Main Author:	Prakasa Rao, Bhagavatula L. S. 1942- (Author)
Format:	Book
Language:	English
Published:	Boca Raton [u.a.] Chapman & Hall 1999
Series:	Monographs on statistics and applied probability 83
Subjects:	Asymptotische analyse Martingalen Semimartingales (Mathematics) Statistiek Stochastic analysis Statistik Mathematical statistics > Asymptotic theory Semimartingales Inferenzstatistik Semimartingal
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

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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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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
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work_keys_str_mv	AT prakasaraobhagavatulals semimartingalesandtheirstatisticalinference

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