Basic principles and applications of probability theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2005
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Auch als Internetausgabe |
| Beschreibung: | 282 S. |
| ISBN: | 3540546863 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV019759820 | ||
| 003 | DE-604 | ||
| 005 | 20060301 | ||
| 007 | t | ||
| 008 | 050405s2005 gw |||| 00||| eng d | ||
| 015 | |a 04,A50,0975 |2 dnb | ||
| 016 | 7 | |a 972601384 |2 DE-101 | |
| 020 | |a 3540546863 |c Pp. : EUR 80.20 |9 3-540-54686-3 | ||
| 035 | |a (OCoLC)249606566 | ||
| 035 | |a (DE-599)BVBBV019759820 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 1 | |a eng |h rus | |
| 044 | |a gw |c XA-DE | ||
| 049 | |a DE-824 |a DE-91G |a DE-634 |a DE-11 |a DE-188 | ||
| 082 | 0 | |a 519.2 | |
| 084 | |a SK 800 |0 (DE-625)143256: |2 rvk | ||
| 084 | |a 510 |2 sdnb | ||
| 084 | |a MAT 600f |2 stub | ||
| 100 | 1 | |a Skorochod, Anatolij V. |d 1930-2011 |e Verfasser |0 (DE-588)128936037 |4 aut | |
| 240 | 1 | 0 | |a Teorija verojatnosteij |
| 245 | 1 | 0 | |a Basic principles and applications of probability theory |c A. V. Skorokhod |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2005 | |
| 300 | |a 282 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Auch als Internetausgabe | ||
| 650 | 4 | |a Wahrscheinlichkeitstheorie | |
| 650 | 0 | 7 | |a Wahrscheinlichkeitstheorie |0 (DE-588)4079013-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Wahrscheinlichkeitstheorie |0 (DE-588)4079013-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 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=013086198&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-013086198 | ||
Datensatz im Suchindex
| _version_ | 1804133235393822720 |
|---|---|
| adam_text | A.V.
SKOROKHOD
BASIC
PRINCIPLES
AND APPLICATIONS
OF
PROBABILITY THEORY
EDITED
BY
YU.V.
PROKHOROV
TRANSLATED
BY
B.
D.
SECKLER
SPRINGER
CONTENTS
I
.
PROBABILITY
.
BASIC NOTIONS
.
STRUCTURE
.
METHODS
...........
1
I1
.
MARKOV
PROCESSES
AND PROBABILITY APPLICATIONS IN ANALYSIS
..................
143
LLL
.
APPLIED PROBABILITY
.........................................
191
AUTHOR INDEX
................................................
275
SUBJECT INDEX
................................................
277
PROBABILITY BASIC NOTIONS STRUCTURE
METHODS
CONTENTS
1
INTRODUCTION
..............................................
5
1.1
THE NATURE
OF
RANDOMNESS
..............................
5
1.1.1
DETERMINISM AND CHAOS
...........................
6
1.1.2 UNPREDICTABILITY AND RANDOMNESS
..................
6
1.1.3 SOURCES
OF
RANDOMNESS
............................
7
1.1.4 THE ROLE
OF
CHANCE
..............................
8
1.2 FORMALIZATION OF RANDOMNESS
............................
9
1.2.1 SELECTION FROM AMONG SEVERAL POSSIBILITIES
EXPERIMENTS
.
EVENTS
..............................
9
1.2.2 RELATIVE FREQUENCIES PROBABILITY AS AN IDEAL
RELATIVE FREQUENCY
...............................
12
1.2.3 THE DEFINITION
OF
PROBABILITY
......................
13
1.3 PROBLEMS
OF
PROBABILITY THEORY
..........................
14
1.3.1
PROBABILITY AND MEASURE THEORY
...................
15
1.3.3 ASYMPTOTIC BEHAVIOR OF STOCHASTIC SYSTEMS
..........
16
1.3.4 STOCHASTIC ANALYSIS
...............................
17
1.3.2 INDEPENDENCE
....................................
15
2
PROBABILITY SPACE
.........................................
19
2.1 FINITE PROBABILITY SPACE
.................................
19
2.1.1 COMBINATORIAL ANALYSIS
...........................
19
2.1.2
CONDITIONAL PROBABILITY
...........................
21
2.1.3 BERNOULLI S SCHEME
.
LIMIT THEOREMS
................
24
2.2 DEFINITION
OF
PROBABILITY SPACE
...........................
27
2.2.1 A-ALGEBRAS
.
PROBABILITY
............................
27
2.2.2 RANDOM VARIABLES
.
EXPECTATION
....................
29
2.2.3 CONDITIONAL EXPECTATION
..........................
31
2.2.4 REGULAR CONDITIONAL DISTRIBUTIONS
..................
34
2.2.5 SPACES
OF
RANDOM VARIABLES
.
CONVERGENCE
...........
35
2.3 RANDOM MAPPINGS
.....................................
38
2.3.1 RANDOM ELEMENTS
................................
38
2
CONTENTS
2.3.2 RANDOM FUNCTIONS
...............................
2.3.3 RANDOM ELEMENTS IN LINEAR SPACES
.................
CONSTRUCTION
OF
PROBABILITY SPACES
.......................
2.4.1 FINITE-DIMENSIONAL SPACE
..........................
2.4.2 FUNCTION SPACES
..................................
2.4.3 LINEAR TOPOLOGICAL SPACES
.
WEAK DISTRIBUTIONS
.......
2.4.4 THE MINLOS-SAZONOV THEOREM
......................
2.4
3
INDEPENDENCE
...............
..........................
3.1.1
INDEPENDENT ALGEBRAS
............................
3.1.4 INDEPENDENT RANDOM VARIABLES
....................
SEQUENCES
OF
INDEPENDENT RANDOM VARIABLES
............
3.2.1
3.2.2 KOLMOGOROV S INEQUALITY
...........................
3.2.3
3.2.4
THE STRONG LAW
OF
LARGE NUMBERS
.................
3.3 RANDOM WALKS
.........................................
3.3.1
THE RENEWAL SCHEME
.............................
3.3.2 RECURRENCY
...
3.3.3
LADDER FUN
....................
3.4 PROCESSES WITH INDEPENDENT INCREMENTS
...................
3.4.1 DEFINITION
......
.............................
3.4.2 STOCHASTICALLY CO
OUS
PROCESSES
.
.
3.4.3 LEVY S FORMULA
..................................
3.5 PRODUCT MEASURES
......................................
ABSOLUTE CONTINUITY AND SINGULARITY
OF
MEASURES
.....
ABSOLUTE CONTINUITY
OF
GAUSSIAN PRODUCT MEASURES
...
3.1 INDEPENDENCE
OF
A-ALGEBRAS
..................
3.1.2
3.1.3
CONDITIONS FOR THE INDEPENDENCE
OF
A-ALGEBRAS
.......
INFINITE SEQUENCES
OF
INDEPENDENT A-ALGEBRAS
.....
3.2
SUMS
OF
INDEPENDENT RANDOM VARIABLES
.............
CONVERGENCE
OF
SERIES
OF
INDEPENDENT RANDOM VARIABLES
3.5.1 DEFINITION
.
.
............................
3.5.2
3.5.3 KAKUTANI S THEOREM
........................
3.5.4
4
GENERAL THEORY OF STOCHASTIC PROCESSES AND
RANDOM FUNCTIONS
........................................
4.1 REGULAR MODIFICATIONS
...................................
4.1.1 SEPARABLE RANDOM FUNCTIONS
......................
4.1.2 CONTINUOUS STOCHASTIC PROCESSES
....................
4.1.3 PROCESSES WITH AT MOST JUMP DISCONTINUITIES
........
4.1.4 MARKOV PROCESSES
................................
4.2 MEASURABILITY
..........................................
4.2.1 EXISTENCE
OF
A
MEASURABLE MODIFICATION
.............
4.2.2 MEAN-SQUARE INTEGRATION
..........................
4.2.3
ORTHOGONAL SERIES
................................
EXPANSION
OF
A RANDOM FUNCTION IN AN
42
44
46
46
47
50
51
53
53
53
55
56
57
59
59
61
63
65
67
67
71
74
78
78
80
83
86
86
87
88
91
93
93
94
96
97
98
100
100
101
103
CONTENTS
3
4.3
ADAPTED PROCESSES
............................
4.3.1
STOPPING TIMES
..................................
105
4.3.2
PROGRESSIVE MEASURABILITY
.........................
106
4.3.3
COMPLETELY MEASURABLE AND PREDICTABLE A-ALGEBRAS
4.3.4
COMPLETELY MEASURABLE AND PREDICTABLE PROCESSES
....
108
4.4.2
INEQUALITIES
.
EXISTENCE OF
4.4.3
CONTINUOUS PARAMETER
. .
STOCHASTIC INTEGRALS AND INTEGRAL REPRESENTATIONS
OF
RANDOM FUNCTIONS
.
.................................
115
4.5.1
RANDOM MEAS
S
................................
115
4.5.2
KARHUNEN S THEOREM
.........
116
4.5.3
SPECTRAL REPRESENTATION
OF
SOME RANDOM FUNCTIONS
.
.
117
4.5
5
LIMIT THEOREMS
..........................................
119
5.1
WEAK CONVERGENCE OF DISTRIBUTIONS
.......................
119
5.1.1
WEAK CONVERGENCE
OF
MEASURES IN METRIC SPACES
.....
119
5.1.2
WEAK COMPACTNESS
...............................
122
5.1.3
WEAK CONVERGENCE
OF
MEASURES IN
RD
...............
123
5.2
ERGODIC THEOREMS
......................................
124
5.2.1
MEASURE-PRESERVING TRANSFORMATIONS
................
124
5.2.2
BIRKHOFF S THEOREM
...............................
126
5.2.3
METRIC TRANSITIVITY
...............................
130
5.3
CENTRAL LIMIT THEOREM AND INVARIANCE PRINCIPLE
............
132
5.3.1
IDENTICALLY DISTRIBUTED TERMS
......................
132
5.3.2
LINDEBERG S THEOREM
.............................
133
5.3.3
DONSKER-PROKHOROV THEOREM
.......................
135
HISTORIC AND BIBLIOGRAPHIC COMMENTS
........................
139
REFERENCES
....................................................
141
|
| any_adam_object | 1 |
| author | Skorochod, Anatolij V. 1930-2011 |
| author_GND | (DE-588)128936037 |
| author_facet | Skorochod, Anatolij V. 1930-2011 |
| author_role | aut |
| author_sort | Skorochod, Anatolij V. 1930-2011 |
| author_variant | a v s av avs |
| building | Verbundindex |
| bvnumber | BV019759820 |
| classification_rvk | SK 800 |
| classification_tum | MAT 600f |
| ctrlnum | (OCoLC)249606566 (DE-599)BVBBV019759820 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01548nam a2200421 c 4500</leader><controlfield tag="001">BV019759820</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20060301 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">050405s2005 gw |||| 00||| eng d</controlfield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">04,A50,0975</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">972601384</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540546863</subfield><subfield code="c">Pp. : EUR 80.20</subfield><subfield code="9">3-540-54686-3</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)249606566</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV019759820</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="1" ind2=" "><subfield code="a">eng</subfield><subfield code="h">rus</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">XA-DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-824</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.2</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 800</subfield><subfield code="0">(DE-625)143256:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">510</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 600f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Skorochod, Anatolij V.</subfield><subfield code="d">1930-2011</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)128936037</subfield><subfield code="4">aut</subfield></datafield><datafield tag="240" ind1="1" ind2="0"><subfield code="a">Teorija verojatnosteij</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Basic principles and applications of probability theory</subfield><subfield code="c">A. V. Skorokhod</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2005</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">282 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Auch als Internetausgabe</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Wahrscheinlichkeitstheorie</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Wahrscheinlichkeitstheorie</subfield><subfield code="0">(DE-588)4079013-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Wahrscheinlichkeitstheorie</subfield><subfield code="0">(DE-588)4079013-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">DNB Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013086198&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-013086198</subfield></datafield></record></collection> |
| id | DE-604.BV019759820 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:05:29Z |
| institution | BVB |
| isbn | 3540546863 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013086198 |
| oclc_num | 249606566 |
| open_access_boolean | |
| owner | DE-824 DE-91G DE-BY-TUM DE-634 DE-11 DE-188 |
| owner_facet | DE-824 DE-91G DE-BY-TUM DE-634 DE-11 DE-188 |
| physical | 282 S. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Springer |
| record_format | marc |
| spelling | Skorochod, Anatolij V. 1930-2011 Verfasser (DE-588)128936037 aut Teorija verojatnosteij Basic principles and applications of probability theory A. V. Skorokhod Berlin [u.a.] Springer 2005 282 S. txt rdacontent n rdamedia nc rdacarrier Auch als Internetausgabe Wahrscheinlichkeitstheorie Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013086198&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Skorochod, Anatolij V. 1930-2011 Basic principles and applications of probability theory Wahrscheinlichkeitstheorie Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4079013-7 |
| title | Basic principles and applications of probability theory |
| title_alt | Teorija verojatnosteij |
| title_auth | Basic principles and applications of probability theory |
| title_exact_search | Basic principles and applications of probability theory |
| title_full | Basic principles and applications of probability theory A. V. Skorokhod |
| title_fullStr | Basic principles and applications of probability theory A. V. Skorokhod |
| title_full_unstemmed | Basic principles and applications of probability theory A. V. Skorokhod |
| title_short | Basic principles and applications of probability theory |
| title_sort | basic principles and applications of probability theory |
| topic | Wahrscheinlichkeitstheorie Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Wahrscheinlichkeitstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013086198&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT skorochodanatolijv teorijaverojatnosteij AT skorochodanatolijv basicprinciplesandapplicationsofprobabilitytheory |