Probability inequalities:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer [u.a.]
2010
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 181 S. 235 mm x 155 mm |
| ISBN: | 9783642052606 9787030255624 |
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MARC
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| 100 | 1 | |a Lin, Zhengyan |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Probability inequalities |c Zhengyan Lin ; Zhidong Bai |
| 264 | 1 | |a Berlin [u.a.] |b Springer [u.a.] |c 2010 | |
| 300 | |a XI, 181 S. |c 235 mm x 155 mm | ||
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| 650 | 4 | |a Inequalities (Mathematics) | |
| 650 | 4 | |a Mathematical statistics | |
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Record in the Search Index
| _version_ | 1804141170188615680 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
CHAPTER 1 ELEMENTARY INEQUALITIES OF PROBABILITIES OF EVENTS 1
1.1 INCLUSION-EXCLUSION FORMULA 1
1.2 COROLLARIES OF THE INCLUSION-EXCLUSION FORMULA 2 1.3 FURTHER
CONSEQUENCES OF THE INCLUSION-EXCLUSION FORMULA - 2 1.4 INEQUALITIES
RELATED TO SYMMETRIC DIFFERENCE 6
1.5 INEQUALITIES RELATED TO INDEPENDENT EVENTS 6
1.6 LOWER BOUND FOR UNION (CHUNG-ERDOES) 8
. REFERENCES 8
CHAPTER 2 INEQUALITIES RELATED TO COMMONLY USED DIS- TRIBUTIONS 9
2.1 INEQUALITIES RELATED TO THE NORMAL D.F. 9
2.2 SLEPIAN TYPE INEQUALITIES 12
2.3 ANDERSON TYPE INEQUALITIES 17
2.4 KHATRI-SIDAK TYPE INEQUALITIES 18
2.5 CORNER PROBABILITY OF NORMAL VECTOR 19
2.6 NORMAL APPROXIMATIONS OF BINOMIAL AND POISSON DISTRI- BUTIONS 20
REFERENCES 22
CHAPTER 3 INEQUALITIES RELATED TO CHARACTERISTIC FUN- CTIONS 23
3.1 INEQUALITIES RELATED ONLY WITH C.F. 23
3.2 INEQUALITIES RELATED TO C.F. AND D.F. 26
3.3 NORMALITY APPROXIMATIONS OF C.F. OF INDEPENDENT SUMS 27
REFERENCES 28
CHAPTER 4 ESTIMATES OF THE DIFFERENCE OF TWO DISTRI- BUTION FUNCTIONS 29
4.1 FOURIER TRANSFORMATION 29
4.2 STEIN-CHEN METHOD 33
4.3 STIELTJES TRANSFORMATION 34
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/997577908
DIGITALISIERT DURCH
IMAGE 2
VIUE CONTENTS
REFERENCES 36
CHAPTER 5 PROBABILITY INEQUALITIES OF RANDOM VARI- ABLES 37
5.1 INEQUALITIES RELATED TO TWO R.V. S 37
5.2 PERTURBATION INEQUALITY 39
5.3 SYMMETRIZATION INEQUALITIES 40
5.4 LEVY INEQUALITY 41
5.5 BICKEL INEQUALITY 42
5.6 UPPER BOUNDS OF TAIL PROBABILITIES OF PARTIAL SUMS 44 5.7 LOWER
BOUNDS OF TAIL PROBABILITIES OF PARTIAL SUMS 44 5.8 TAIL PROBABILITIES
FOR MAXIMUM PARTIAL SUMS 45
5.9 TAIL PROBABILITIES FOR MAXIMUM PARTIAL SUMS (CONTIN- UATION) 46
5.10 REFLECTION INEQUALITY OF TAIL PROBABILITY (HOFFMANN- J0RGENSEN) 47
5.11 PROBABILITY OF MAXIMAL INCREMENT (SHAO) 48
5.12 MOGULSKII MINIMAL INEQUALITY 49
5.13 WILKS INEQUALITY 50
REFERENCES * 50
CHAPTER 6 BOUNDS OF PROBABILITIES IN TERMS OF MO- MENTS 51
6.1 CHEBYSHEV-MARKOV TYPE INEQUALITIES 51
6.2 LOWER BOUNDS 52
6.3 SERIES OF TAIL PROBABILITIES 53
6.4 KOLMOGOROV TYPE INEQUALITIES 54
6.5 GENERALIZATION OF KOLMOGOROV INEQUALITY FOR A SUBMAR- TINGALE 56
6.6 RENYI-HAJEK TYPE INEQUALITIES 57
6.7 CHERNOFF INEQUALITY 60
6.8 FUK AND NAGAEV INEQUALITY - ** 62
6.9 BURKHOLDER INEQUALITY 63
6.10 COMPLETE CONVERGENCE OF PARTIAL SUMS 65
REFERENCES * 65
CHAPTER 7 EXPONENTIAL TYPE ESTIMATES OF PROBABILITIES * * * 67 7.1
EQUIVALENCE OF EXPONENTIAL ESTIMATES 67
7.2 PETROV EXPONENTIAL INEQUALITIES 68
IMAGE 3
CONTENTS IX
7.3 HOEFFDING INEQUALITY 70
7.4 BENNETT INEQUALITY 72
7.5 BERNSTEIN INEQUALITY 73
7.6 EXPONENTIAL BOUNDS FOR SUMS OF BOUNDED VARIABLES 74 7.7 KOLMOGOROV
INEQUALITIES 75
7.8 PROKHOROV INEQUALITY 79
7.9 EXPONENTIAL INEQUALITIES BY CENSORING 80
7.10 TAIL PROBABILITY OF WEIGHTED SUMS * * * 82
REFERENCES 83
CHAPTER 8 MOMENT INEQUALITIES RELATED TO ONE OR TWO VARIABLES 84
8.1 MOMENTS OF TRUNCATION 84
8.2 EXPONENTIAL MOMENT OF BOUNDED VARIABLES 84
8.3 HOLDER TYPE INEQUALITIES 85
8.4 JENSEN TYPE INEQUALITIES 86
8.5 DISPERSION INEQUALITY OF CENSORED VARIABLES 87
8.6 MONOTONICITY OF MOMENTS OF SUMS 88
8.7 SYMMETRIZATION MOMENT INEQUATILIES 88
8.8 KIMBALL INEQUALITY 89
8.9 EXPONENTIAL MOMENT OF NORMAL VARIABLE 90
8.10 INEQUATILIES OF NONNEGATIVE VARIABLE 93
8.11 FREEDMAN INEQUALITY 94
8.12 EXPONENTIAL MOMENT OF UPPER TRUNCATED VARIABLES 95
REFERENCES 96
CHAPTER 9 MOMENT ESTIMATES OF (MAXIMUM OF) SUMS OF RANDOM VARIABLES 97
9.1 ELEMENTARY INEQUALITIES 97
9.2 MINKOWSKI TYPE INEQUALITIES 99
9.3 THE CASE 1 R ^ 2 100
9.4 THE CASE R 2 101
9.5 JACK-KNIFED VARIANCE 105
9.6 KHINTCHINE INEQUALITY * 106
9.7 MARCINKIEWICZ-ZYGMUND-BURKHOLDER TYPE INEQUALITIES 108 9.8 SKOROKHOD
INEQUALITIES I LL
9.9 MOMENTS OF WEIGHTED SUMS 112
9.10 DOOB CROSSING INEQUALITIES 113
IMAGE 4
X CONTENTS
9.11 MOMENTS OF MAXIMAL PARTIAL SUMS 114
9.12 DOOB INEQUALITIES 115
9.13 EQUIVALENCE CONDITIONS FOR MOMENTS 117
9.14 SERFLING INEQUALITIES 123
9.15 AVERAGE FILL RATE 127
REFERENCES * 128
CHAPTER 10 INEQUALITIES RELATED TO MIXING SEQUENCES 130 10.1 COVARIANCE
ESTIMATES FOR MIXING SEQUENCES 131
10.2 TAIL PROBABILITY ON A-MIXING SEQUENCE 134
10.3 ESTIMATES OF 4-TH MOMENT ON P-MIXING SEQUENCE 135 10.4 ESTIMATES OF
VARIANCES OF INCREMENTS OF P-MIXING SEQUENCE 136
10.5 BOUNDS OF 2 + 5-TH MOMENTS OF INCREMENTS OF P-MIXING SEQUENCE 138
10.6 TAIL PROBABILITY ON ^-MIXING SEQUENCE 140
10.7 BOUNDS OF 2 + 5-TH MOMENT OF INCREMENTS OF IP-MIXING SEQUENCE *
142
10.8 EXPONENTIAL ESTIMATES OF PROBABILITY ON (P- MIXING SEQUENCE 143
REFERENCES 148
CHAPTER 11 INEQUALITIES RELATED TO ASSOCIATIVE VARI- ABLES * 149
11.1 COVARIANCE OF PQD VARAIBLES 149
11.2 PROBABILITY OF QUADRANT ON PA (NA) SEQUENCE 150 11.3 ESTIMATES OF
C.F. S ON LPQD (LNQD) SEQUENCE 151 11.4 MAXIMAL PARTIAL SUMS OF PA
SEQUENCE 152
11.5 VARIANCE OF INCREMENT OF LPQD SEQUENCE 153
11.6 EXPECTATION OF CONVEX FUNCTION OF SUM OF NA SEQUENCE 154
11.7 MARCINKIEWICZ-ZYGMUND-BURKHOLDER INEQUALITY FOR NA SEQUENCE * * 156
REFERENCES 157
CHAPTER 12 INEQUALITIES ABOUT STOCHASTIC PROCESSES AND BANACH SPACE
VALUED RANDOM VARIABLES 158 12.1 PROBABILITY ESTIMATES OF SUPREMUMS OF A
WIENER PROCESS 158
IMAGE 5
CONTENTS XI
12.2 PROBABILITY ESTIMATE OF SUPREMUM OF A POISSON PROCESS 162
12.3 FERNIQUE INEQUALITY 164
12.4 BORELL INEQUALITY 167
12.5 TAIL PROBABILITY OF GAUSSIAN PROCESS 168
12.6 TAIL PROBABILITY OF RANDOMLY SIGNED INDEPENDENT PROCESSES 168
12.7 TAIL PROBABILITY OF ADAPTIVE PROCESS 170
12.8 TAIL PROBABILITY ON SUBMARTINGALE 172
12.9 TAIL PROBABILITY OF INDEPENDENT SUM IN B-SPACE 173 12.10
ISOPERIMETRIC INEQUALITIES 173
12.11 EHRHARD INEQUALITY 174
12.12 TAIL PROBABILITY OF NORMAL VARIABLE IN B-SPACE 175 12.13 GAUSSIAN
MEASURE ON SYMMETRIC CONVEX SETS 175 12.14 EQUIVALENCE OF MOMENTS OF
B-GAUSSIAN VARIABLES 176 12.15 CONTRACTION PRINCIPLE 176
12.16 SYMMETRIZATION INEQUALITIES IN B-SPACE 178
12.17 DECOUPLING INEQUALITY 178
REFERENCES 180
|
| any_adam_object | 1 |
| author | Lin, Zhengyan Bai, Zhidong 1943- |
| author_GND | (DE-588)140643133 |
| author_facet | Lin, Zhengyan Bai, Zhidong 1943- |
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| id | DE-604.BV036101222 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:11:37Z |
| institution | BVB |
| isbn | 9783642052606 9787030255624 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018991578 |
| oclc_num | 462919494 |
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| owner_facet | DE-91G DE-BY-TUM DE-824 DE-703 DE-19 DE-BY-UBM DE-11 |
| physical | XI, 181 S. 235 mm x 155 mm |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer [u.a.] |
| record_format | marc |
| spelling | Lin, Zhengyan Verfasser aut Probability inequalities Zhengyan Lin ; Zhidong Bai Berlin [u.a.] Springer [u.a.] 2010 XI, 181 S. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Inequalities (Mathematics) Mathematical statistics Probabilities Stochastische Ungleichung (DE-588)4700404-6 gnd rswk-swf Stochastische Ungleichung (DE-588)4700404-6 s DE-604 Bai, Zhidong 1943- Verfasser (DE-588)140643133 aut Erscheint auch als Online-Ausgabe 978-3-642-05261-3 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018991578&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lin, Zhengyan Bai, Zhidong 1943- Probability inequalities Inequalities (Mathematics) Mathematical statistics Probabilities Stochastische Ungleichung (DE-588)4700404-6 gnd |
| subject_GND | (DE-588)4700404-6 |
| title | Probability inequalities |
| title_auth | Probability inequalities |
| title_exact_search | Probability inequalities |
| title_full | Probability inequalities Zhengyan Lin ; Zhidong Bai |
| title_fullStr | Probability inequalities Zhengyan Lin ; Zhidong Bai |
| title_full_unstemmed | Probability inequalities Zhengyan Lin ; Zhidong Bai |
| title_short | Probability inequalities |
| title_sort | probability inequalities |
| topic | Inequalities (Mathematics) Mathematical statistics Probabilities Stochastische Ungleichung (DE-588)4700404-6 gnd |
| topic_facet | Inequalities (Mathematics) Mathematical statistics Probabilities Stochastische Ungleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018991578&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT linzhengyan probabilityinequalities AT baizhidong probabilityinequalities |