Probability theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
1997
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 414 S. Ill., graph. Darst. |
| ISBN: | 9810222130 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV012990891 | ||
| 003 | DE-604 | ||
| 005 | 20130228 | ||
| 007 | t | ||
| 008 | 000216s1997 si ad|| |||| 00||| eng d | ||
| 020 | |a 9810222130 |9 981-02-2213-0 | ||
| 035 | |a (OCoLC)40074453 | ||
| 035 | |a (DE-599)BVBBV012990891 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 1 | |a eng |h rus | |
| 044 | |a si |c XB-SG | ||
| 049 | |a DE-703 |a DE-521 |a DE-11 |a DE-83 | ||
| 050 | 0 | |a QA273.R853 1997 | |
| 082 | 0 | |a 519.2 |2 21 | |
| 082 | 0 | |a 519.2 21 | |
| 084 | |a QH 170 |0 (DE-625)141536: |2 rvk | ||
| 084 | |a SK 800 |0 (DE-625)143256: |2 rvk | ||
| 084 | |a 60-01 |2 msc | ||
| 100 | 1 | |a Rotarʹ, Vladimir I. |e Verfasser |0 (DE-588)134277945 |4 aut | |
| 245 | 1 | 0 | |a Probability theory |c Vladimir Rotar |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 1997 | |
| 300 | |a XVIII, 414 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Probabilités |2 ram | |
| 650 | 7 | |a Waarschijnlijkheidstheorie |2 gtt | |
| 650 | 4 | |a Probabilities | |
| 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 GBV Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008851367&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-008851367 | ||
Datensatz im Suchindex
| _version_ | 1804127688987770880 |
|---|---|
| adam_text | IMAGE 1
PROBABILITY
THEORY
VLADIMIR ROTAR CENTRAL ECONOMIC MATHEMATICAL INSTITUTE RUSSIAN ACADEMY
OF SCIENCES
WORLD SCIENTIFIC SINGAPORE * NEW JERSEY * LONDON * HONG KONG
NIEDER3ACHS. STAATS. U. U
IMAGE 2
CONTENTS
PREFACE TO THE ENGLISH EDITION XI
INTRODUCTION XIII
0. A SPACE OF ELEMENTARY EVENTS XVII
PART I. ELEMENTARY THEORY
CHAPTER 1. BASIC NOTIONS 2
1. PROBABILITY DISTRIBUTIONS ON DISCRETE SPACES OF ELEMENTARY EVENTS 2
ELEMENTARY PROBABILITIES. EVENTS AND THEIR PROBABILITIES. PROPERTIES OF
PROBABILITY MEASURES. SUMMATION THEOREM. CONTINUITY PROPERTY.
PROBABILITY SPACE.
APPENDIX TO SECTION 1. PARTICULAR CLASSICAL SCHEMES 7 PERMUTATIONS.
PARTITIONS INTO GROUPS. ALLOCATIONS OF PARTICLES INTO CELLS. RANDOM
SAMPLING WITH AND WITHOUT REPLACEMENT. 2. INDEPENDENCE OF EVENTS AND
SEQUENCES OF TRIALS 12
DEFINITIONS AND EXAMPLES. BERNOULLI S SCHEME. THE MULTI- NOMIAL SCHEME.
3. CONDITIONAL PROBABILITY 17
DEFINITIONS AND EXAMPLES. THE FORMULA OF TOTAL PROBABILITY. RUIN
PROBLEM. BAYES FORMULA. 4. RANDOM VARIABLES 24
ONE-DIMENSIONAL RANDOM VARIABLES. JOINT DISTRIBUTIONS OF RANDOM
VARIABLES. CONVOLUTIONS. CONDITIONAL DISTRIBUTIONS. 5. EXPECTATION 30
DEFINITIONS AND EXAMPLES. PROPERTIES OF EXPECTATION. CONDITIONAL
EXPECTATIONS. THE FORMULA OF TOTAL EXPECTATION. REGRESSION. THE
CONDITIONAL EXPECTATION WITH RESPECT TO A COM-
PLETE SET OF DISJOINT EVENTS. 6. VARIANCE 40
DEFINITIONS AND EXAMPLES. TWO PROPERTIES OF VARIANCE. STAN- DARD SCALING
(OR NORMALIZATION). BIENAYME S EQUALITY. SUMS OF INDEPENDENT RANDOM
VARIABLES. ARITHMETIC MEAN OF RANDOM VARIABLES. 7. HIGHER MOMENTS AND
INEQUALITIES FOR DEVIATIONS 46
MOMENTS. JENSEN S INEQUALITY. BASIC INEQUALITY FOR DEVIATIONS.
IMAGE 3
CHAPTER 2. THE LAW OF LARGE NUMBERS. LIMIT THEOREMS FOR
BERNOULLI S SCHEME 50
8. THE LAW OF LARGE NUMBERS 50
CONVERGENCE IN PROBABILITY. THE WEAK LAW OF LARGE NUMBERS. CONVERGENCE
OF EXPECTATIONS. BERNSTEIN S POLYNOMIALS.
APPENDIX TO SECTION 8 55
ZERO-SUM GAMES. ST. PETERSBURG S PARADOX. RELATIVE STABILITY. UTILITY
FUNCTION. THE SIMPLEST MODEL OF INSURANCE. 9. DE MOIVRE-LAPLACE THEOREMS
60
THE LOCAL THEOREM. THE INTEGRAL THEOREM. ON THE ACCURACY OF
APPROXIMATION. PROOF OF THE LOCAL THEOREM. 10. THE POISSON THEOREM AND
THE SIMPLEST FLOW OF EVENTS 65 THE POISSON THEOREM. THE SIMPLEST FLOW OF
EVENTS. THE CON-
VOLUTION OF POISSON S DISTRIBUTIONS.
CHAPTER 3. GENERATING FUNCTIONS AND RANDOM WALKS 70 11. GENERATING
FUNCTIONS (G.F. S) 70
DEFINITION AND BASIC PROPERTIES. THE GENERATING FUNCTION OF THE SUM OF
RANDOM VARIABLES. THE GENERATING FUNCTION OF THE SUM OF A RANDOM NUMBER
OF RANDOM VARIABLES. THE EXTINCTION PROB- LEM OR THE GALTON-WATSON
PROCESS. THE GENERATING FUNCTION OF A CONVOLUTION. CONTINUITY THEOREM.
THE POISSON THEOREM FOR NONIDENTICALLY DISTRIBUTED SUMMANDS. 12. ON
RANDOM WALKS 78
RETURN TO ZERO . THE ARCSINE LAW. THE NUMBER OF DRAWS .
PART II. GENERAL THEORY
CHAPTER 1. FOUNDATIONS OF THE THEORY 88
1. PRELIMINARY CONSTRUCTIONS 88
PROBABILITY MEASURE. RANDOM VARIABLES AND THEIR EXPECTA- TIONS. 2.
PROBABILITY DISTRIBUTIONS 93
EVENTS. MEASURES AND PROBABILITIES. CONTINUITY PROPERTY. PRODUCTS OF
PROBABILITY SPACES. 3. RANDOM VARIABLES 103
MEASURABILITY. CONVERGENCE OF RANDOM VARIABLES. THE LEBESGUE INTEGRAL OR
EXPECTATION OF AN ELEMENTARY RANDOM VARIABLE. THE LEBESGUE INTEGRAL:
EXPECTATION OF AN ARBITRARY
IMAGE 4
RANDOM VARIABLE. THE INTEGRAL OVER A SET AND THE RESTRICTION OF
A MEASURE. PASSAGE TO THE LIMIT UNDER THE INTEGRAL SIGN. COM- PARING THE
RIEMANN AND LEBESGUE INTEGRALS. INTEGRALS WITH RESPECT TO A-FINITE
MEASURES. THE THEOREM ON ITERATED INTE- GRALS. ABSOLUTE CONTINUITY AND
THE RADON-NIKODYM THEORY.
CONCLUDING REMARKS.
CHAPTER 2. DISTRIBUTIONS ON FINITE-DIMENSIONAL SPACES 120 4.
DISTRIBUTIONS OF RANDOM VARIABLES 120
INDUCED DISTRIBUTIONS. ABSOLUTELY CONTINUOUS DISTRIBUTIONS. DISCRETE
DISTRIBUTIONS. MIXTURES. DISTRIBUTION FUNCTIONS (D.F. S). SINGULAR
DISTRIBUTIONS. THE LEBESGUE EXPANSION. LEBESGUE-STIELTJES INTEGRAL.
LINEAR TRANSFORMS OF RANDOM VARI- ABLES AND TYPES OF DISTRIBUTIONS. 5.
DISTRIBUTIONS OF RANDOM VECTORS 135
DEFINITIONS AND EXAMPLES. LINEAR TRANSFORMS OF RANDOM VEC- TORS.
INDEPENDENT RANDOM VARIABLES. CONVOLUTIONS. 6. SOME PARTICULAR
DISTRIBUTIONS ON THE REAL LINE 144
THE UNIFORM TYPE. THE NORMAL TYPE. THE EXPONENTIAL TYPE AND THE LACK OF
MEMORY PROPERTY. GAMMA-DISTRIBUTIONS. A CONNECTION BETWEEN THE POISSON
AND EXPONENTIAL DISTRIBUTIONS. X 2 -DISTRIBUTION. 7. COVARIANCE ANALYSIS
AND MULTIVARIATE NORMAL DISTRIBUTION 157
COVARIANCE. COVARIANCE MATRIX. PROPERTIES OF COVARIANCE MA- TRICES. THE
METHOD OF PRINCIPAL COMPONENTS OR MAIN FACTORS. STANDARD NORMAL
DISTRIBUTION IN R FC . NORMAL DISTRIBUTION IN R*. 8. CONVERGENCE OF
DISTRIBUTIONS 163
WEAK OR PROPER CONVERGENCE. CONVERGENCE OF MOMENTS. STOCHASTIC
BOUNDEDNESS AND THE SELECTION THEOREM. IMPROPER CONVERGENCE. PROXIMITY
OF DISTRIBUTIONS. OTHER TYPES OF CON-
VERGENCE OF DISTRIBUTIONS. MULTIDIMENSIONAL CASE. PROOFS OF THEOREMS
1-1 AND LEMMA 4. PROOF OF THEOREM 2. PROOFS OF THEOREMS 3-3 . PROOFS OF
THEOREMS 4-5. 9. COMPARISON OF DISTRIBUTIONS 181
PREFERENCE RELATION OR ORDERING. CALCULABILITY. PRIMARY CONDITIONS.
COMPARISON BASED ON EXPECTATION AND VARIANCE. CONTINUITY CONDITIONS.
EXPECTATION AS A CRITERION. UTILITY FUNCTION. UTILITY FUNCTION AND
CONDITION AL.
IMAGE 5
JENSEN S INEQUALITY. UTILITY FUNCTION AND CONDITION A2.
GENERALIZATION OF THEOREM 2. ALLAIS PARADOX AND NONLINEAR FUNCTIONAL.
CHAPTER 3. CONDITIONAL DISTRIBUTIONS 200
10. CONDITIONAL DISTRIBUTIONS AND EXPECTATIONS 201
THE DISCRETE CASE. THE ABSOLUTELY CONTINUOUS CASE. THE GEN- ERAL CASE.
PROPERTIES OF CONDITIONAL EXPECTATION. THE FORMULA OF TOTAL EXPECTATION.
A REGRESSION FUNCTION AND A PREDICTION PROBLEM. LINEAR REGRESSION. THE
CONVOLUTION FORMULA. PROD-
UCT OF INDEPENDENT RANDOM VARIABLES. RATIO OF INDEPENDENT RANDOM
VARIABLES. A SYSTEM OF EQUATIONS WITH RANDOM CO- EFFICIENTS. THE STUDENT
DISTRIBUTION. 11. CONDITIONAL EXPECTATIONS WITH RESPECT TO C-ALGEBRAS
OF EVENTS 217
BASIC NOTIONS. PROPERTIES OF CONDITIONAL EXPECTATION. CON- DITIONAL
DISTRIBUTIONS. DERIVATION OF REPRESENTATION (5) FROM SECTION 10.
CHAPTER 4. SOME KINDS OF DEPENDENCE 226
12. CONDITIONALLY INDEPENDENT AND EXCHANGEABLE RANDOM VARIABLES 226
MIXTURES OF DISTRIBUTIONS. CONDITIONALLY INDEPENDENT RANDOM VARIABLES.
SYMMETRICALLY DEPENDENT OR EXCHANGEABLE RANDOM VARIABLES. 13.
MARTINGALES 233
DEFINITIONS, PROPERTIES AND EXAMPLES. MARKOV MOMENTS AND BOUNDARY
PROBLEMS. CONTINUITY PROPERTIES. PROOF OF DE FINETTI THEOREM. 14. MARKOV
CHAINS 243
BASIC NOTIONS AND PROPERTIES. ERGODICITY PROPERTY.
CHAPTER 5. LIMIT THEOREMS 260
15. LIMIT THEOREMS FOR MAXIMA AND MINIMA. REGULARLY VARYING FUNCTIONS
261
THE STATEMENT OF THE PROBLEM. PRELIMINARY RESULT. REGULARLY VARYING
FUNCTIONS. LIMIT THEOREMS FOR IDENTICALLY DISTRIBUTED RANDOM VARIABLES.
PROOFS OF THEOREMS 1-2. THE GENERAL SCHEME.- * -.,
IMAGE 6
16. CHARACTERISTIC FUNCTIONS AND THE FIRST LIMIT THEOREMS
FOR SUMS 273
THE LAPLACE TRANSFORM. ELEMENTARY PROPERTIES OF CHARACTER- ISTIC
FUNCTIONS. EXAMPLES OF CHARACTERISTIC FUNCTIONS. CHAR- ACTERISTIC
FUNCTIONS OF LATTICE DISTRIBUTIONS. THE CHARACTERISTIC FUNCTION OF A
MIXTURE OF DISTRIBUTIONS. UNIQUENESS AND CON- TINUITY THEOREMS. ON
SMOOTHNESS OF CHARACTERISTIC FUNCTIONS. THE LAW OF LARGE NUMBERS FOR
IDENTICALLY DISTRIBUTED SUMMANDS. CONVERGENCE OF SUMS OF IDENTICALLY
DISTRIBUTED SUMMANDS TO A NORMAL DISTRIBUTION: LEVY S THEOREM. A LIMIT
THEOREM FOR SUMS OF ROTATIONS.
17. CHARACTERISTIC FUNCTIONS, INVERSION THEOREMS 287
LATTICE DISTRIBUTIONS. ABSOLUTELY CONTINUOUS DISTRIBUTIONS. THE INVERSE
IN THE GENERAL CASE: SMOOTHING. AN INVERSION FOR- MULA BASED ON THE
DIRICHLET INTEGRAL. TRUNCATION INEQUALITIES. PROOFS OF THE CONTINUITY
THEOREMS. GENERALIZATION OF THE CON- TINUITY THEOREM.
18. LIMIT THEOREMS FOR SUMS. THE CASE OF FINITE VARIANCES 301
PRELIMINARY STATEMENT OF THE PROBLEM. TRIANGULAR ARRAYS. CONDITIONS FOR
NORMAL CONVERGENCE: SUFFICIENCY. CONDITIONS FOR NORMAL CONVERGENCE:
NECESSITY. CONVERGENCE TO THE POISSON
DISTRIBUTION. THE THEOREM ON PROXIMITY OF CONVOLUTIONS. LINDEBERG S
THEOREM FOLLOWS FROM THEOREM 5. PROOF OF THEOREM 5. PROOF OF FELLER S
THEOREM. DEVELOPMENT OF THEOREM 4 FROM THEOREM 5.
19. STABLE DISTRIBUTIONS 318
STABILITY PROPERTY. THE STABILITY OF LIMITING DISTRIBUTIONS. THE CASE OF
FINITE VARIANCES. SYMMETRIC STABLE DISTRIBUTIONS. ON THE DENSITY OF
SYMMETRIC STABLE DISTRIBUTIONS. STABLE DISTRIBUTIONS
IN THE GENERAL CASE. CONVERGENCE TO STABLE DISTRIBUTIONS. PROOF OF THE
THEOREM ON THE NUMBER OF DRAWS. ADDITIONAL REMARKS.
20. LIMIT THEOREMS FOR SUMS. THE GENERAL CASE 341
CENTERING. RESCALING. THE GENERAL SCHEME OF SUMMATION. PROOF OF THEOREM
1. CONVERGENCE TO STABLE DISTRIBUTIONS.
21. ON LARGE DEVIATIONS 354
THE STATEMENT OF THE PROBLEM. A THEOREM ON LARGE DEVIATIONS. AN
INEQUALITY FOR LARGE DEVIATIONS. PROOF OF THEOREM 2.
IMAGE 7
22. CHARACTERISTIC FUNCTIONS AND LIMIT THEOREMS IN THE
MULTIDIMENSIONAL CASE 358
CHARACTERISTIC FUNCTIONS. UNIQUENESS AND CONTINUITY THEOREMS. THE
MULTIDIMENSIONAL ANALOG OF LEVY S THEOREM. LIMIT THEOREMS FOR SOME
NONLINEAR FUNCTIONS OF MANY RANDOM ARGUMENTS. 23. LIMIT THEOREMS FOR
DEPENDENT SUMMANDS 366
PRELIMINARY EXAMPLES. RANDOM SUMMANDS WITH TWO VALUES. LIMIT THEOREMS
FOR AN INFINITE SEQUENCE OF SYMMETRICALLY DE- PENDENT RANDOM VARIABLES.
LIMIT THEOREMS FOR MARTINGALES.
THE DERIVATION OF THEOREM 6 FROM THEOREM 7. PROOF OF THEOREM 7. LIMIT
THEOREMS FOR RANDOM VARIABLES DEFINED ON A MARKOV CHAIN. 24. NONLINEAR
LIMIT THEOREMS 382
THE GENERAL STATEMENT OF THE PROBLEM. MULTILINEAR FORMS AND POLYNOMIALS
OF RANDOM VARIABLES.
CHAPTER 6. ALMOST SURE BEHAVIOR OF SUMS OF RANDOM VARIABLES 390
25. THE BORELL-CANTELLI THEOREM AND THE ZERO-ONE LAW 390 THE
BORELL-CANTELLI THEOREM. THE ZERO-ONE LAW. 26. THE STRONG LAW OF LARGE
NUMBERS (SLLN) AND THE LAW OF THE ITERATED LOGARITHM 394
THE STRONG LAW OF LARGE NUMBERS: NECESSITY. THE KOLMOGOROV AND LEVY
INEQUALITIES. A THEOREM ON CONVERGENCE OF MARTIN- GALES OR A CRITERION
OF CONVERGENCE OF SERIES. THE STRONG LAW OF LARGE NUMBERS: SUFFICIENCY.
THE STRONG LAW OF LARGE NUMBERS FOR INDEPENDENT IDENTICALLY DISTRIBUTED
RANDOM VARIABLES. THE LAW OF THE ITERATED LOGARITHM. 27. THE LAW OF
LARGE NUMBERS AND STOCHASTIC OPTIMIZATION
PROBLEMS 405
THE SIMPLEST STOCHASTIC OPTIMIZATION SCHEME. THE CASE OF DE- PENDENT
OBSERVATIONS. ON THE GENERAL SCHEME OF STOCHASTIC OPTIMIZATION.
REFERENCES 412
|
| any_adam_object | 1 |
| author | Rotarʹ, Vladimir I. |
| author_GND | (DE-588)134277945 |
| author_facet | Rotarʹ, Vladimir I. |
| author_role | aut |
| author_sort | Rotarʹ, Vladimir I. |
| author_variant | v i r vi vir |
| building | Verbundindex |
| bvnumber | BV012990891 |
| callnumber-first | Q - Science |
| callnumber-label | QA273 |
| callnumber-raw | QA273.R853 1997 |
| callnumber-search | QA273.R853 1997 |
| callnumber-sort | QA 3273 R853 41997 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 170 SK 800 |
| ctrlnum | (OCoLC)40074453 (DE-599)BVBBV012990891 |
| dewey-full | 519.2 519.221 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 519.2 21 |
| dewey-search | 519.2 519.2 21 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01507nam a2200421 c 4500</leader><controlfield tag="001">BV012990891</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20130228 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">000216s1997 si ad|| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9810222130</subfield><subfield code="9">981-02-2213-0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)40074453</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV012990891</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</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">si</subfield><subfield code="c">XB-SG</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield><subfield code="a">DE-521</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA273.R853 1997</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.2</subfield><subfield code="2">21</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.2 21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">QH 170</subfield><subfield code="0">(DE-625)141536:</subfield><subfield code="2">rvk</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">60-01</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Rotarʹ, Vladimir I.</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)134277945</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Probability theory</subfield><subfield code="c">Vladimir Rotar</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Singapore [u.a.]</subfield><subfield code="b">World Scientific</subfield><subfield code="c">1997</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVIII, 414 S.</subfield><subfield code="b">Ill., graph. Darst.</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="650" ind1=" " ind2="7"><subfield code="a">Probabilités</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Waarschijnlijkheidstheorie</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Probabilities</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">GBV 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=008851367&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:BVB01-008851367</subfield></datafield></record></collection> |
| id | DE-604.BV012990891 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:37:20Z |
| institution | BVB |
| isbn | 9810222130 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008851367 |
| oclc_num | 40074453 |
| open_access_boolean | |
| owner | DE-703 DE-521 DE-11 DE-83 |
| owner_facet | DE-703 DE-521 DE-11 DE-83 |
| physical | XVIII, 414 S. Ill., graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Rotarʹ, Vladimir I. Verfasser (DE-588)134277945 aut Probability theory Vladimir Rotar Singapore [u.a.] World Scientific 1997 XVIII, 414 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Probabilités ram Waarschijnlijkheidstheorie gtt Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008851367&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rotarʹ, Vladimir I. Probability theory Probabilités ram Waarschijnlijkheidstheorie gtt Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4079013-7 |
| title | Probability theory |
| title_auth | Probability theory |
| title_exact_search | Probability theory |
| title_full | Probability theory Vladimir Rotar |
| title_fullStr | Probability theory Vladimir Rotar |
| title_full_unstemmed | Probability theory Vladimir Rotar |
| title_short | Probability theory |
| title_sort | probability theory |
| topic | Probabilités ram Waarschijnlijkheidstheorie gtt Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Probabilités Waarschijnlijkheidstheorie Probabilities Wahrscheinlichkeitstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008851367&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT rotarʹvladimiri probabilitytheory |