Basic stochastic processes: a course through exercises
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
London [u.a.]
Springer
1998
|
| Schriftenreihe: | Springer undergraduate mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 225 S. graph. Darst. |
| ISBN: | 3540761756 |
Internformat
MARC
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| 020 | |a 3540761756 |c Pb. : DM 55.00 |9 3-540-76175-6 | ||
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| 245 | 1 | 0 | |a Basic stochastic processes |b a course through exercises |c Zdzisław Brzézniak and Tomasz Zastawniak |
| 264 | 1 | |a London [u.a.] |b Springer |c 1998 | |
| 300 | |a X, 225 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer undergraduate mathematics series | |
| 650 | 4 | |a Procesos estocásticos | |
| 650 | 4 | |a Stochastic processes | |
| 650 | 0 | 7 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |2 gnd |9 rswk-swf |
| 655 | 7 | |8 1\p |0 (DE-588)4151278-9 |a Einführung |2 gnd-content | |
| 689 | 0 | 0 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Zastawniak, Tomasz |d 1959- |e Verfasser |0 (DE-588)120071231 |4 aut | |
| 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=008239230&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1807501212733407232 |
|---|---|
| adam_text |
CONTENTS
1.
REVIEW
OF
PROBABILITY
.
1
1.1
EVENTS
AND
PROBABILITY
.
1
1.2
RANDOM
VARIABLES
.
3
1.3
CONDITIONAL
PROBABILITY
AND
INDEPENDENCE
.
8
1.4
SOLUTIONS
.
10
2.
CONDITIONAL
EXPECTATION
.
17
2.1
CONDITIONING
ON
AN
EVENT
.
17
2.2
CONDITIONING
ON
A
DISCRETE
RANDOM
VARIABLE
.
19
2.3
CONDITIONING
ON
AN
ARBITRARY
RANDOM
VARIABLE
.
22
2.4
CONDITIONING
ON
A
A-FIELD
.
27
2.5
GENERAL
PROPERTIES
.
29
2.6
VARIOUS
EXERCISES
ON
CONDITIONAL
EXPECTATION
.
31
2.7
SOLUTIONS
.
33
3.
MARTINGALES
IN
DISCRETE
TIME
.
45
3.1
SEQUENCES
OF
RANDOM
VARIABLES
.
45
3.2
FILTRATIONS
.
46
3.3
MARTINGALES
.
48
3.4
GAMES
OF
CHANCE
.
51
3.5
STOPPING
TIMES
.
54
3.6
OPTIONAL
STOPPING
THEOREM
.
58
3.7
SOLUTIONS
.
61
4.
MARTINGALE
INEQUALITIES
AND
CONVERGENCE
.
67
4.1
DOOB
'
S
MARTINGALE
INEQUALITIES
.
68
X
CONTENTS
4.2
DOOB
'
S
MARTINGALE
CONVERGENCE
THEOREM
.
71
4.3
UNIFORM
INTEGRABILITY
AND
L
1
CONVERGENCE
OF
MARTINGALES
.
73
4.4
SOLUTIONS
.
80
5.
MARKOV
CHAINS
.
85
5.1
FIRST
EXAMPLES
AND
DEFINITIONS
.
86
5.2
CLASSIFICATION
OF
STATES
.
101
5.3
LONG-TIME
BEHAVIOUR
OF
MARKOV
CHAINS:
GENERAL
CASE
.
108
5.4
LONG-TIME
BEHAVIOUR
OF
MARKOV
CHAINS
WITH
FINITE
STATE
SPACE
.
114
5.5
SOLUTIONS
.
119
6.
STOCHASTIC
PROCESSES
IN
CONTINUOUS
TIME
.
139
6.1
GENERAL
NOTIONS
.
139
6.2
POISSON
PROCESS
.
140
6.2.1
EXPONENTIAL
DISTRIBUTION
AND
LACK
OF
MEMORY
.
140
6.2.2
CONSTRUCTION
OF
THE
POISSON
PROCESS
.
142
6.2.3
POISSON
PROCESS
STARTS
FROM
SCRATCH
AT
TIME
T
.
145
6.2.4
VARIOUS
EXERCISES
ON
THE
POISSON
PROCESS
.
148
6.3
BROWNIAN
MOTION
.
150
6.3.1
DEFINITION
AND
BASIC
PROPERTIES
.
151
6.3.2
INCREMENTS
OF
BROWNIAN
MOTION
.
153
6.3.3
SAMPLE
PATHS
.
156
6.3.4
DOOB
'
S
MAXIMAL
L
2
INEQUALITY
FOR
BROWNIAN
MOTION
.
159
6.3.5
VARIOUS
EXERCISES
ON
BROWNIAN
MOTION
.
160
6.4
SOLUTIONS
.
161
7.
IT6
STOCHASTIC
CALCULUS
.
179
7.1
ITO
STOCHASTIC
INTEGRAL:
DEFINITION
.
180
7.2
EXAMPLES
.
189
7.3
PROPERTIES
OF
THE
STOCHASTIC
INTEGRAL
.
190
7.4
STOCHASTIC
DIFFERENTIAL
AND
ITO
FORMULA
.
193
7.5
STOCHASTIC
DIFFERENTIAL
EQUATIONS
.
202
7.6
SOLUTIONS
.
209
INDEX
.
223 |
| any_adam_object | 1 |
| author | Brzeźniak, Zdzisław 1958- Zastawniak, Tomasz 1959- |
| author_GND | (DE-588)120071193 (DE-588)120071231 |
| author_facet | Brzeźniak, Zdzisław 1958- Zastawniak, Tomasz 1959- |
| author_role | aut aut |
| author_sort | Brzeźniak, Zdzisław 1958- |
| author_variant | z b zb t z tz |
| building | Verbundindex |
| bvnumber | BV012162758 |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274.B78 1999 |
| callnumber-search | QA274.B78 1999 |
| callnumber-sort | QA 3274 B78 41999 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 820 |
| ctrlnum | (OCoLC)885136205 (DE-599)BVBBV012162758 |
| dewey-full | 519.221 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 21 |
| dewey-search | 519.2 21 |
| dewey-sort | 3519.2 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre | 1\p (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV012162758 |
| illustrated | Illustrated |
| indexdate | 2024-08-16T00:18:01Z |
| institution | BVB |
| isbn | 3540761756 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008239230 |
| oclc_num | 885136205 |
| open_access_boolean | |
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| owner_facet | DE-739 DE-824 DE-706 DE-521 DE-634 |
| physical | X, 225 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer undergraduate mathematics series |
| spelling | Brzeźniak, Zdzisław 1958- Verfasser (DE-588)120071193 aut Basic stochastic processes a course through exercises Zdzisław Brzézniak and Tomasz Zastawniak London [u.a.] Springer 1998 X, 225 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer undergraduate mathematics series Procesos estocásticos Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Stochastischer Prozess (DE-588)4057630-9 s DE-604 Zastawniak, Tomasz 1959- Verfasser (DE-588)120071231 aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008239230&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Brzeźniak, Zdzisław 1958- Zastawniak, Tomasz 1959- Basic stochastic processes a course through exercises Procesos estocásticos Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4151278-9 |
| title | Basic stochastic processes a course through exercises |
| title_auth | Basic stochastic processes a course through exercises |
| title_exact_search | Basic stochastic processes a course through exercises |
| title_full | Basic stochastic processes a course through exercises Zdzisław Brzézniak and Tomasz Zastawniak |
| title_fullStr | Basic stochastic processes a course through exercises Zdzisław Brzézniak and Tomasz Zastawniak |
| title_full_unstemmed | Basic stochastic processes a course through exercises Zdzisław Brzézniak and Tomasz Zastawniak |
| title_short | Basic stochastic processes |
| title_sort | basic stochastic processes a course through exercises |
| title_sub | a course through exercises |
| topic | Procesos estocásticos Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Procesos estocásticos Stochastic processes Stochastischer Prozess Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008239230&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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