Continuous-parameter time series:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston
De Gruyter
[2024]
|
| Schriftenreihe: | De Gruyter studies in mathematics
Volume 98 |
| Schlagworte: | |
| Online-Zugang: | https://www.degruyter.com/isbn/9783111324999 Inhaltsverzeichnis |
| Beschreibung: | XXI, 498 Seiten Illustrationen 24 cm x 17 cm |
| ISBN: | 9783111324999 3111324990 |
Internformat
MARC
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| 003 | DE-604 | ||
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| 020 | |a 9783111324999 |c : EUR 124.95 (DE) (freier Preis), EUR 124.95 (AT) (freier Preis) |9 978-3-11-132499-9 | ||
| 020 | |a 3111324990 |9 3-11-132499-0 | ||
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| 044 | |a gw |c XA-DE-BE | ||
| 049 | |a DE-29T | ||
| 084 | |8 1\p |a 510 |2 23sdnb | ||
| 100 | 1 | |a Brockwell, Peter J. |d 1937-2023 |e Verfasser |0 (DE-588)171133188 |4 aut | |
| 245 | 1 | 0 | |a Continuous-parameter time series |c Peter J. Brockwell† and Alexander M. Lindner |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2024] | |
| 300 | |a XXI, 498 Seiten |b Illustrationen |c 24 cm x 17 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter studies in mathematics |v Volume 98 | |
| 650 | 0 | 7 | |a Zeitreihenanalyse |0 (DE-588)4067486-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |2 gnd |9 rswk-swf |
| 653 | |a Zeitfolgen | ||
| 653 | |a Hilbert Räume | ||
| 653 | |a Stochastische Prozesses | ||
| 653 | |a L'evy Prozesse | ||
| 653 | |a Deterministische Funktionen | ||
| 653 | |a Time series | ||
| 653 | |a Hilabert Space | ||
| 653 | |a Second order stochastic processes | ||
| 653 | |a L'evy processes | ||
| 653 | |a deterministic functions. | ||
| 689 | 0 | 0 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |D s |
| 689 | 0 | 1 | |a Zeitreihenanalyse |0 (DE-588)4067486-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Lindner, Alexander |d 1973- |e Verfasser |0 (DE-588)121156532 |4 aut | |
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| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, PDF |z 9783111325033 |
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| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035189733&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-035189733 | |
Datensatz im Suchindex
| _version_ | 1816971325405659136 |
|---|---|
| adam_text |
CONTENTS
PREFACE
-
VII
LIST
OF
SYMBOLS
AND
ABBREVIATIONS
-
XVII
1
TIME
SERIES
-
1
1.1
EXAMPLES
OF
TIME
SERIES
-
1
1.2
STOCHASTIC
PROCESSES
-
4
1.3
WEAK
AND
STRICT
STATIONARITY
-
9
1.4
EXISTENCE
OF
BROWNIAN
MOTION
AND
THE
POISSON
PROCESS
-
14
1.5
EXERCISES
-
21
2
HILBERT
SPACES
-
22
2.1
INNER-PRODUCT
SPACES
AND
THEIR
PROPERTIES
-
22
2.2
HILBERT
SPACES
-
25
2.3
THE
PROJECTION
THEOREM
-
28
2.4
ORTHONORMAL
SETS
-
32
2.5
MEAN-SQUARE
CONVERGENCE,
CONDITIONAL
EXPECTATION
AND
BEST
LINEAR
PREDICTION
IN
S
-
34
2.6
BEST
LINEAR
ESTIMATION
OF
RANDOM
VECTORS
IN
S
-
37
2.7
HILBERT
SPACE
ISOMORPHISMS
-
39
2.8
FOURIER
TRANSFORMS
-
40
2.8.1
THE
FOURIER
TRANSFORM
OF
AN
L1
FUNCTION
-
41
2.8.2
THE
FOURIER
TRANSFORM
OF
AN
L
2
FUNCTION
-
45
2.9
EXERCISES
-
49
3
SECOND-ORDER
STOCHASTIC
PROCESSES
-
52
3.1
THE
MEAN
AND
AUTOCOVARIANCE
FUNCTIONS
-
52
3.2
MEAN-SQUARE
CONTINUITY
-
54
3.3
MEAN-SQUARE
DIFFERENTIABILITY
-
56
3.4
MEAN-SQUARE
RIEMANN
INTEGRABILITY
-
59
3.5
MEAN-SQUARE
AND
PATHWISE
PROPERTIES
-
61
3.6
EXERCISES
-
61
4
ORTHOGONAL
INCREMENT
PROCESSES
-
63
4.1
PRELIMINARIES
-
63
4.2
DEFINITION
AND
ELEMENTARY
PROPERTIES
-
63
4.3
INTEGRATION
WITH
RESPECT
TO
AN
OIP
-
66
4.4
OIP
PROCESSES
WITH
DENSITIES
-
71
4.5
THE
FOURIER
TRANSFORM
OF
AN
OIP
PROCESS
-
75
4.6
EXERCISES
-
77
XIV
-
CONTENTS
5
5.1
5.2
5.3
5.4
5.5
SPECTRAL
THEORY
OF
MSC
STATIONARY
PROCESSES
-
78
SPECTRAL
REPRESENTATION
OF
THE
AUTOCOVARIANCE
FUNCTION
-
78
THE
SPECTRAL
REPRESENTATION
OF
A
STATIONARY
PROCESS
-
82
INVERSION
FORMULAE
-
90
LINEAR
TRANSFORMATIONS
OF
MSC
STATIONARY
PROCESSES
-
93
EXERCISES
-
95
6
6.1
6.2
6.3
MEAN-SQUARE
LINEAR
PREDICTION
OF
WEAKLY
STATIONARY
PROCESSES
-
97
THE
DISCRETE-TIME
CASE
-
97
THE
CONTINUOUS-TIME
CASE
-
105
EXERCISES
-
127
7
7.1
7.2
7.3
7.4
7.5
SECOND-ORDER
CARMA
PROCESSES
-
130
DEFINITION
AND
PROPERTIES
-
130
THE
WOLD-KARHUNEN
REPRESENTATION
-
134
PREDICTION
-
144
R-PROGRAMS
TO
COMPUTE
THE
KERNEL
AND
AUTOCOVARIANCE
FUNCTION
-
154
EXERCISES
-
157
8
8.1
8.2
INFINITELY
DIVISIBLE
DISTRIBUTIONS
-
158
INFINITE
DIVISIBILITY
IN
LEVY
PROCESSES
-
158
FIRST
EXAMPLES
AND
ELEMENTARY
PROPERTIES
OF
INFINITELY
DIVISIBLE
DISTRIBUTIONS
-
160
8.3
8.4
THE
DISTINGUISHED
LOGARITHM
AND
N
TH
ROOT
-
164
EXERCISES
-
172
9
9.1
9.2
THE
LEVY-KHINTCHINE
FORMULA
FOR
INFINITELY
DIVISIBLE
DISTRIBUTIONS
-
173
THE
LEVY-KHINTCHINE
FORMULA
-
173
LINEAR
TRANSFORMATIONS
AND
INDEPENDENCE
OF
INFINITELY
DIVISIBLE
DISTRIBUTIONS
-
192
9.3
9.4
CONVERGENCE
OF
INFINITELY
DIVISIBLE
DISTRIBUTIONS
-
196
EXERCISES
-
201
10
10.1
10.2
10.3
10.4
LEVY
PROCESSES
-
203
DEFINITION,
ELEMENTARY
PROPERTIES
AND
EXAMPLES
-
203
LEVY
PROCESSES
IN
LAW
AND
INFINITELY
DIVISIBLE
DISTRIBUTIONS
-
214
EXISTENCE
OF
LEVY
PROCESSES
-
220
EXERCISES
-
228
11
DISTRIBUTIONAL
PROPERTIES
OF
LEVY
PROCESSES
AND
THE
STRONG
LAW
OF
LARGE
NUMBERS
-
229
11.1
THE
MARKOV
PROPERTY
AND
TIME
REVERSAL
OF
LEVY
PROCESSES
-
229
CONTENTS
-
XV
11.2
11.3
MOMENTS
OF
LEVY
PROCESSES
AND
INFINITELY
DIVISIBLE
DISTRIBUTIONS
-
230
STRONG
LAW
OF
LARGE
NUMBERS
AND
A
FURTHER
GROWTH
CONDITION
FOR
LEVY
PROCESSES
-
244
11.4
EXERCISES
-
246
12
12.1
12.2
12.3
12.4
LEVY
PROCESSES
AS
RANDOM
ELEMENTS
AND
THEIR
JUMP
STRUCTURE
-
248
LEVY
PROCESSES
AS
RANDOM
ELEMENTS
IN
THE
SPACE
OF
CADLAG
FUNCTIONS
-
248
CHARACTERIZATIONS
OF
THE
POISSON
PROCESS
AND
OF
BROWNIAN
MOTION
-
259
THE
JUMP
STRUCTURE
OF
LEVY
PROCESSES
-
265
EXERCISES
-
285
13
13.1
13.2
13.3
13.4
THE
LEVY-ITO
DECOMPOSITION
OF
LEVY
PROCESSES
AND
CONSEQUENCES
-
287
THE
LEVY-ITO
DECOMPOSITION
OF
A
LEVY
PROCESS
-
287
LEVY
PROCESSES
OF
FINITE
VARIATION
-
297
SUBORDINATORS
-
304
EXERCISES
-
312
14
14.1
14.2
14.3
14.4
14.5
EXAMPLES
OF
LEVY
PROCESSES
-
314
STABLE
DISTRIBUTIONS
AND
STABLE
LEVY
PROCESSES
-
314
THE
GAMMA
PROCESS
-
328
PROCESSES
OBTAINED
BY
SUBORDINATION
-
330
THE
INVERSE
GAUSSIAN
AND
RELATED
LEVY
PROCESSES
-
338
EXERCISES
-
343
15
INTEGRATION
OF
DETERMINISTIC
FUNCTIONS
WITH
RESPECT
TO
LEVY
PROCESSES
-
346
15.1
LEBESGUE-STIELTJES
INTEGRAL
WITH
RESPECT
TO
LEVY
PROCESSES
OF
FINITE
VARIATION
-
346
15.2
15.3
INTEGRATION
WITH
RESPECT
TO
ONE-DIMENSIONAL
LEVY
PROCESSES
-
354
THE
INTEGRAL
FOR
MATRIX-VALUED
INTEGRANDS
AND
IRD-VALUED
LEVY
PROCESSES
-
364
15.4
EXERCISES
-
368
16
16.1
16.2
16.3
16.4
16.5
THE
DISTRIBUTION
OF
THE
INTEGRAL
AND
CONSEQUENCES
-
369
THE
CHARACTERISTIC
FUNCTION
OF
THE
INTEGRAL
-
369
DISTRIBUTIONAL
PROPERTIES
OF
THE
INTEGRAL
-
379
CONTINUOUS-TIME
MOVING
AVERAGE
PROCESSES
-
386
IMPROPER
INTEGRALS
-
388
EXERCISES
-
390
17
17.1
ORNSTEIN-UHLENBECK
PROCESSES
-
391
SOLUTION
OF
THE
ORNSTEIN-UHLENBECK
EQUATION
-
391
XVI
-
CONTENTS
BIBLIOGRAPHY
-
485
17.2
17.3
17.4
STATIONARY
ORNSTEIN-UHLENBECK
PROCESSES
-
395
MARKOV-STABLE
ORNSTEIN-UHLENBECK
PROCESSES
-
405
EXERCISES
-
408
18
LEVY-DRIVEN
CARMA
PROCESSES:
DEFINITION,
EXISTENCE,
UNIQUENESS
AND
PROPERTIES
-
410
18.1
18.2
18.3
18.4
18.5
18.6
18.7
18.8
INTRODUCTION
-
410
DEFINITION
AND
EXISTENCE
-
411
UNIQUENESS
AND
THE
A-SAMPLED
SEQUENCE
-
419
SECOND-ORDER
PROPERTIES
WHEN
EI^
2
CO
-
425
CAUSALITY
-
429
THE
CANONICAL
STATE
VECTOR
-
432
THE
A-SAMPLED
SEQUENCE
K
A
,
WHEN
E^I
2
OO
-
435
EXERCISES
-
441
19
19.1
QML
ESTIMATION
FOR
CARMA
PROCESSES
-
443
QML
ESTIMATION
FOR
CARMA
PROCESSES
BASED
ON
OBSERVATIONS
AT
FIXED
TIMES
TOUT
-
443
19.2
19.3
19.4
19.5
19.6
QML
ESTIMATION
FOR
REGULARLY
SAMPLED
CARMA
PROCESSES
-
448
THE
EMBEDDING
PROBLEM
-
449
EXAMPLES,
STOCHASTIC
VOLATILITY
-
458
SIMULATION
OF
CAUSAL
CARMA
PROCESSES
-
466
ASYMPTOTIC
DISTRIBUTION
OF
QML
ESTIMATORS
FOR
A
CARMA(P,P
-1)
PROCESS
-
469
19.7
19.8
ESTIMATING
THE
LEVY
INCREMENTS
-
474
EXERCISES
-
477
A
APPENDIX:
R
PROGRAMS
FOR
GENERATION
OF
LEVY
INCREMENTS
-
479
INDEX
-
489 |
| any_adam_object | 1 |
| author | Brockwell, Peter J. 1937-2023 Lindner, Alexander 1973- |
| author_GND | (DE-588)171133188 (DE-588)121156532 |
| author_facet | Brockwell, Peter J. 1937-2023 Lindner, Alexander 1973- |
| author_role | aut aut |
| author_sort | Brockwell, Peter J. 1937-2023 |
| author_variant | p j b pj pjb a l al |
| building | Verbundindex |
| bvnumber | BV049849885 |
| ctrlnum | (OCoLC)1454762843 (DE-599)DNB1322999430 |
| format | Book |
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| id | DE-604.BV049849885 |
| illustrated | Illustrated |
| indexdate | 2024-11-28T13:01:26Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783111324999 3111324990 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035189733 |
| oclc_num | 1454762843 |
| open_access_boolean | |
| owner | DE-29T |
| owner_facet | DE-29T |
| physical | XXI, 498 Seiten Illustrationen 24 cm x 17 cm |
| publishDate | 2024 |
| publishDateSearch | 2024 |
| publishDateSort | 2024 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter studies in mathematics |
| series2 | De Gruyter studies in mathematics |
| spelling | Brockwell, Peter J. 1937-2023 Verfasser (DE-588)171133188 aut Continuous-parameter time series Peter J. Brockwell† and Alexander M. Lindner Berlin ; Boston De Gruyter [2024] XXI, 498 Seiten Illustrationen 24 cm x 17 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematics Volume 98 Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Zeitfolgen Hilbert Räume Stochastische Prozesses L'evy Prozesse Deterministische Funktionen Time series Hilabert Space Second order stochastic processes L'evy processes deterministic functions. Stochastischer Prozess (DE-588)4057630-9 s Zeitreihenanalyse (DE-588)4067486-1 s DE-604 Lindner, Alexander 1973- Verfasser (DE-588)121156532 aut Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, EPUB 9783111325200 Erscheint auch als Online-Ausgabe, PDF 9783111325033 De Gruyter studies in mathematics Volume 98 (DE-604)BV000005407 98 X:MVB https://www.degruyter.com/isbn/9783111324999 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035189733&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p vlb 20240309 DE-101 https://d-nb.info/provenance/plan#vlb |
| spellingShingle | Brockwell, Peter J. 1937-2023 Lindner, Alexander 1973- Continuous-parameter time series De Gruyter studies in mathematics Zeitreihenanalyse (DE-588)4067486-1 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4067486-1 (DE-588)4057630-9 |
| title | Continuous-parameter time series |
| title_auth | Continuous-parameter time series |
| title_exact_search | Continuous-parameter time series |
| title_full | Continuous-parameter time series Peter J. Brockwell† and Alexander M. Lindner |
| title_fullStr | Continuous-parameter time series Peter J. Brockwell† and Alexander M. Lindner |
| title_full_unstemmed | Continuous-parameter time series Peter J. Brockwell† and Alexander M. Lindner |
| title_short | Continuous-parameter time series |
| title_sort | continuous parameter time series |
| topic | Zeitreihenanalyse (DE-588)4067486-1 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Zeitreihenanalyse Stochastischer Prozess |
| url | https://www.degruyter.com/isbn/9783111324999 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035189733&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005407 |
| work_keys_str_mv | AT brockwellpeterj continuousparametertimeseries AT lindneralexander continuousparametertimeseries AT walterdegruytergmbhcokg continuousparametertimeseries |