Statistics of random processes: 1 General theory
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin [u.a.]
Springer
[2001]
|
| Ausgabe: | Second, revised and expanded edition |
| Schriftenreihe: | Applications of mathematics
5 |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008558173&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XV, 427 Seiten |
| ISBN: | 3540639292 |
Internformat
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| 100 | 1 | |a Lipcer, Robert S. |d 1936- |0 (DE-588)122035003 |4 aut | |
| 240 | 1 | 0 | |a Statistika slučajnych processov |
| 245 | 1 | 0 | |a Statistics of random processes |n 1 |p General theory |c R. S. Liptser ; A. N. Shiryayev. Transl. by A. B. Aries |
| 250 | |a Second, revised and expanded edition | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c [2001] | |
| 300 | |a XV, 427 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Applications of mathematics |v 5 | |
| 490 | 0 | |a Applications of mathematics |v ... | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0048 MAT 605f 2001 A 9537-1(2) 0102 MAT 605f 2001 A 9537-1(2) 0104 MAT 605f 2001 A 9537-1(2) |
|---|---|
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| DE-BY-TUM_location | LSB 01 |
| DE-BY-TUM_media_number | 040010228309 040020086411 040020272155 |
| _version_ | 1821931950212907009 |
| adam_text | Table of Contents
Preface to the Second Edition V
Introduction 1
1. Essentials of Probability Theory and Mathematical
Statistics 11
1.1 Main Concepts of Probability Theory 11
1.2 Random Processes: Basic Notions 20
1.3 Markov Times 25
1.4 Brownian Motion Processes 30
1.5 Some Notions from Mathematical Statistics 34
2. Martingales and Related Processes: Discrete Time 39
2.1 Supermartingales and Submartingales on a Finite Time Interval 39
2.2 Submartingales on an Infinite Time Interval,
and the Theorem of Convergence 45
2.3 Regular Martingales: Levy s Theorem 47
2.4 Invariance of the Supermartingale Property for Markov Times:
Riesz and Doob Decompositions 50
3. Martingales and Related Processes: Continuous Time .... 57
3.1 Right Continuous Supermartingales 57
3.2 Basic Inequalities, the Theorem of Convergence, and Invari¬
ance of the Supermartingale Property for Markov Times 60
3.3 Doob Meyer Decomposition for Supermartingales 64
3.4 Some Properties of Predictable Increasing Processes 74
4. The Wiener Process, the Stochastic Integral over the Wiener
Process, and Stochastic Differential Equations 85
4.1 The Wiener Process as a Square Integrable Martingale 85
4.2 Stochastic Integrals: Ito Processes 92
4.3 Ito s Formula 123
4.4 Strong and Weak Solutions of Stochastic Differential Equationsl32
X Table of Contents
5. Square Integrable Martingales and Structure
of the Punctionals on a Wiener Process 161
5.1 Doob Meyer Decomposition for Square Integrable Martingales 161
5.2 Representation of Square Integrable Martingales 170
5.3 The Structure of Functional of a Wiener Process 174
5.4 Stochastic Integrals over Square Integrable Martingales 182
5.5 Integral Representations of the Martingales which are Con¬
ditional Expectations and the Fubini Theorem for Stochastic
Integrals 193
5.6 The Structure of Functional of Processes
of the Diffusion Type 200
6. Nonnegative Supermartingales and Martingales,
and the Girsanov Theorem 219
6.1 Nonnegative Supermartingales 219
6.2 Nonnegative Martingales 228
6.3 The Girshanov Theorem and its Generalization 238
7. Absolute Continuity of Measures corresponding to the Ito
Processes and Processes of the Diffusion Type 251
7.1 The Ito Processes, and the Absolute Continuity
of their Measures with respect to Wiener Measure 251
7.2 Processes of the Diffusion Type: the Absolute Continuity
of their Measures with respect to Wiener Measure 257
7.3 The Structure of Processes whose Measure is Absolutely
Continuous with Respect to Wiener Measure 271
7.4 Representation of the Ito Processes as Processes
of the Diffusion Type, Innovation Processes, and the Struc¬
ture of Functionals on the Ito Process 273
7.5 The Case of Gaussian Processes 279
7.6 The Absolute Continuity of Measures of the Ito Processes
with respect to Measures Corresponding to Processes of the
Diffusion Type 286
7.7 The Cameron Martin Formula 297
7.8 The Cramer Wolfowitz Inequality 299
7.9 An Abstract Version of the Bayes Formula 303
8. General Equations of Optimal Nonlinear Filtering,
Interpolation and Extrapolation of Partially Observable
Random Processes 317
8.1 Filtering: the Main Theorem 317
8.2 Filtering: Proof of the Main Theorem 319
8.3 Filtering of Diffusion Markov Processes 326
8.4 Equations of Optimal Nonlinear Interpolation 329
8.5 Equations of Optimal Nonlinear Extrapolation 331
Table of Contents XI
8.6 Stochastic Differential Equations with Partial Derivatives for
the Conditional Density (the Case of Diffusion Markov Pro¬
cesses) 334
9. Optimal Filtering, Interpolation and Extrapolation
of Markov Processes with a Countable Number of States . 351
9.1 Equations of Optimal Nonlinear Filtering 351
9.2 Forward and Backward Equations of Optimal Nonlinear
Interpolation 363
9.3 Equations of Optimal Nonlinear Extrapolation 368
9.4 Examples 371
10. Optimal Linear Nonstationary Filtering 375
10.1 The Kalman Bucy Method 375
10.2 Martingale Proof of the Equations of Linear Nonstationary
Filtering 389
10.3 Equations of Linear Nonstationary Filtering:
the Multidimensional Case 392
10.4 Equations for an Almost Linear Filter for Singular B o B .... 400
Bibliography 409
Index 425
|
| any_adam_object | 1 |
| author | Lipcer, Robert S. 1936- Širjaev, Alʹbert N. 1934- |
| author_GND | (DE-588)122035003 (DE-588)12203502X |
| author_facet | Lipcer, Robert S. 1936- Širjaev, Alʹbert N. 1934- |
| author_role | aut aut |
| author_sort | Lipcer, Robert S. 1936- |
| author_variant | r s l rs rsl a n š an anš |
| building | Verbundindex |
| bvnumber | BV012601581 |
| classification_rvk | SK 820 |
| classification_tum | MAT 605f |
| ctrlnum | (OCoLC)174565005 (DE-599)BVBBV012601581 |
| dewey-full | 519.2/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/3 |
| dewey-search | 519.2/3 |
| dewey-sort | 3519.2 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Second, revised and expanded edition |
| format | Book |
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| id | DE-604.BV012601581 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:33:05Z |
| institution | BVB |
| isbn | 3540639292 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008558173 |
| oclc_num | 174565005 |
| open_access_boolean | |
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| physical | XV, 427 Seiten |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series | Applications of mathematics |
| series2 | Applications of mathematics |
| spellingShingle | Lipcer, Robert S. 1936- Širjaev, Alʹbert N. 1934- Statistics of random processes Applications of mathematics |
| title | Statistics of random processes |
| title_alt | Statistika slučajnych processov |
| title_auth | Statistics of random processes |
| title_exact_search | Statistics of random processes |
| title_full | Statistics of random processes 1 General theory R. S. Liptser ; A. N. Shiryayev. Transl. by A. B. Aries |
| title_fullStr | Statistics of random processes 1 General theory R. S. Liptser ; A. N. Shiryayev. Transl. by A. B. Aries |
| title_full_unstemmed | Statistics of random processes 1 General theory R. S. Liptser ; A. N. Shiryayev. Transl. by A. B. Aries |
| title_short | Statistics of random processes |
| title_sort | statistics of random processes general theory |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008558173&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013209908 (DE-604)BV000895226 |
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Handapparate (nicht verfügbar)
| Signatur: |
0048 MAT 605f 2001 A 9537-1(2) Lageplan |
|---|---|
| Exemplar 1 | Dauerhaft ausgeliehen Ausgeliehen – Rückgabe bis: 31.12.9999 |
Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 605f 2001 A 9537-1(2) Lageplan 0104 MAT 605f 2001 A 9537-1(2) Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |
| Exemplar 1 | Nicht ausleihbar Am Standort |