Measure theory and filtering: introduction and applications
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2004
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge series in statistical and probabilistic mathematics
[15] |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | X, 258 S. |
| ISBN: | 0521838037 9780521838030 9781107410718 |
Internformat
MARC
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| 245 | 1 | 0 | |a Measure theory and filtering |b introduction and applications |c Lakhdar Aggoun ; Robert J. Elliott |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2004 | |
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Datensatz im Suchindex
| _version_ | 1804133774498201600 |
|---|---|
| adam_text | Contents
Preface
page
їх
Part I Theory
1
1
Basic probability concepts
3
1.1
Random experiments and probabilities
3
1.2
Conditional probabilities and independence
9
1.3
Random variables
14
1.4
Conditional expectations
28
1.5
Problems
34
2
Stochastic processes
38
2.1
Definitions and general results
38
2.2
Stopping times
46
2.3
Discrete time martingales
50
2.4
Doob decomposition
56
2.5
Continuous time martingales
59
2.6
Doob—Meyer decomposition
62
2.7
Brownian motion
70
2.8
Brownian motion process with drift
72
2.9
Brownian paths
72
2.10
Poisson
process
75
2.11
Problems
75
3
Stochastic calculus
79
3.1
Introduction
79
3.2
Quadratic variations
80
3.3
Simple examples of stochastic integrals
87
3.4
Stochastic integration with respect to a Brownian motion
90
3.5
Stochastic integration with respect to general martingales
94
3.6
The
Ito
formula for semimartingales
97
3.7
The
Ito
formula for Brownian motion
108
3.8
Representation results I - 1
3.9
Random measures
-
3.10
Problems 127
vi
Contents
4
Change
of measures
131
4.1
Introduction
131
4.2
Measure change for discrete time processes
134
4.3
Girsanov s theorem
145
4.4
The single jump process
150
4.5
Change of parameter in
poisson
processes
157
4.6
Poisson
process with drift
161
4.7
Continuous-time Markov chains
163
4.8
Problems
165
Part II Applications
167
169
169
169
169
175
177
178
180
190
196
206
211
215
6
Financial applications
217
6.1
Volatility estimation
217
6.2
Parameter estimation
221
6.3
Filtering a price process
222
6.4
Parameter estimation for a modified
Kalman
filter
223
6.5
Estimating the implicit interest rate of a risky asset
229
7
A genetics model
235
7.1
Introduction
235
7.2
Recursive estimates
235
7.3
Approximate formulae
239
8
Hidden populations
242
8.1
Introduction
242
8.2
Distribution estimation
243
8.3
Parameter estimation
246
8.4
Pathwise estimation
247
8.5
A Markov chain model
248
Kalman
filtering
5.1
Introduction
5.2
Discrete-time scalar dynamics
5.3
Recursive estimation
5.4
Vector dynamics
5.5
The EM algorithm
5.6
Discrete-time model parameter estimation
5.7
Finite-dimensional filters
5.8
Continuous-time vector dynamics
5.9
Continuous-time model parameters estimation
5.10
Direct parameter estimation
5.11
Continuous-time nonlinear filtering
5.12
Problems
Contents
vii
8.6
Recursive parameter estimation
250
8.7
A tags loss model
250
8.8
Gaussian noise approximation
253
References
255
Index
257
Measure Theory and Filtering
Introduction and Applications
The estimation of noisily observed states from a sequence of data has traditionally incor¬
porated ideas from Hubert spaces and calculus-based probability theory. As conditional
expectation is the key concept, the correct setting for filtering theory is that of a probabil¬
ity space. Graduate engineers, mathematicians, and those working in quantitative finance
wishing to use filtering techniques will find in the first half of this book an accessible
introduction to measure theory, stochastic calculus, and stochastic processes, with particular
emphasis on martingales and Brownian motion. Exercises are included, solutions to which
are available from www.cambridge.org. The book then provides an excellent user s guide
to filtering: basic theory is followed by a thorough treatment of
Kalman
filtering, including
recent results that exend the
Kalman
filter to provide parameter estimates. These ideas are
then applied to problems arising in finance, genetics, and population modelling in three sep¬
arate chapters, making this a comprehensive resource for both practitioners and researchers.
Lakhdar Aggoun is Associate Professor in the Department of Mathematics and Statistics
at Sultan Qabos University, Oman.
Robert Elliott is RBC Financial Group Professor of Finance at the University of Calgary,
Canada.
|
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| author | Aggoun, Lakhdar 1952- Elliott, Robert J. 1940- |
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| dewey-raw | 515/.42 |
| dewey-search | 515/.42 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
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| series2 | Cambridge series in statistical and probabilistic mathematics |
| spelling | Aggoun, Lakhdar 1952- Verfasser (DE-588)1034844849 aut Measure theory and filtering introduction and applications Lakhdar Aggoun ; Robert J. Elliott 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2004 X, 258 S. txt rdacontent n rdamedia nc rdacarrier Cambridge series in statistical and probabilistic mathematics [15] Hier auch später erschienene, unveränderte Nachdrucke Filtros de kalman larpcal Kalman, Filtrage de Kalman-filters gtt Maattheorie gtt Medida e integração larpcal Mesure, Théorie de la Kalman filtering Measure theory Kalman-Filter (DE-588)4130759-8 gnd rswk-swf Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Integrationstheorie (DE-588)4138369-2 s DE-604 Maßtheorie (DE-588)4074626-4 s Kalman-Filter (DE-588)4130759-8 s Elliott, Robert J. 1940- Verfasser (DE-588)129338745 aut Cambridge series in statistical and probabilistic mathematics [15] (DE-604)BV011442366 15 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013526503&sequence=000005&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013526503&sequence=000006&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Aggoun, Lakhdar 1952- Elliott, Robert J. 1940- Measure theory and filtering introduction and applications Cambridge series in statistical and probabilistic mathematics Filtros de kalman larpcal Kalman, Filtrage de Kalman-filters gtt Maattheorie gtt Medida e integração larpcal Mesure, Théorie de la Kalman filtering Measure theory Kalman-Filter (DE-588)4130759-8 gnd Integrationstheorie (DE-588)4138369-2 gnd Maßtheorie (DE-588)4074626-4 gnd |
| subject_GND | (DE-588)4130759-8 (DE-588)4138369-2 (DE-588)4074626-4 |
| title | Measure theory and filtering introduction and applications |
| title_auth | Measure theory and filtering introduction and applications |
| title_exact_search | Measure theory and filtering introduction and applications |
| title_full | Measure theory and filtering introduction and applications Lakhdar Aggoun ; Robert J. Elliott |
| title_fullStr | Measure theory and filtering introduction and applications Lakhdar Aggoun ; Robert J. Elliott |
| title_full_unstemmed | Measure theory and filtering introduction and applications Lakhdar Aggoun ; Robert J. Elliott |
| title_short | Measure theory and filtering |
| title_sort | measure theory and filtering introduction and applications |
| title_sub | introduction and applications |
| topic | Filtros de kalman larpcal Kalman, Filtrage de Kalman-filters gtt Maattheorie gtt Medida e integração larpcal Mesure, Théorie de la Kalman filtering Measure theory Kalman-Filter (DE-588)4130759-8 gnd Integrationstheorie (DE-588)4138369-2 gnd Maßtheorie (DE-588)4074626-4 gnd |
| topic_facet | Filtros de kalman Kalman, Filtrage de Kalman-filters Maattheorie Medida e integração Mesure, Théorie de la Kalman filtering Measure theory Kalman-Filter Integrationstheorie Maßtheorie |
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