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Shiryaev A.N. — Probability
Shiryaev A.N. — Probability

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Название: Probability

Автор: Shiryaev A.N.

Аннотация:

This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks, martingales, Markov chains, ergodic theory, weak convergence of probability measures, stationary stochastic processes, and the Kalman-Bucy filter. Many examples are discussed in detail, and there are a large number of exercises. The book is accessible to advanced undergraduates and can be used as a text for self-study. This new edition contains substantial revisions and updated references. The reader will find a deeper study of topics such as the distance between probability measures, metrization of weak convergence, and contiguity of probability measures. Proofs for a number of some important results which were merely stated in the first edition have been added. The author included new material on the probability of large deviations, and on the central limit theorem for sums of dependent random variables.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 1995

Количество страниц: 644

Добавлена в каталог: 11.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$L^2$-theory      Chap.VI 415
$\Lambda$ (condition)      338
$\mathscr{D}$-measurable      76
$\mathscr{F}$-measurable      170
$\pi$      225
$\sigma$-additive      134
A posteriori probability      27
a priori probability      27
a.e.      185
a.s.      185
Absolute continuity with respect to P      195 524
Absolute moment      182
Absolutely continuous, distributions      155
Absolutely continuous, functions      156
Absolutely continuous, measures      155
Absolutely continuous, probability measures      195 524
Absolutely continuous, random variables      171
Absorbing      113 588
Accessible state      569
Algebra induced by a decomposition      12
Algebra of events      12 128
Algebra of sets      132 139
Algebra, $\sigma-$      133 139
Algebra, correspondence with decomposition      82
Algebra, smallest      140
Algebra, tail      380
Almost everywhere      185
Almost invariant      407
Almost periodic      417
Almost surely      185
Amplitude      418
Aperiodic state      572
Appropriate sets, principle of      141
Arcsine law      102
Arithmetic properties      569
Asymptotic algebra      380
Asymptotic properties      573
Asymptotically, infinitesimal      337
Asymptotically, unbiased      443
Asymptotics      536
atoms      12
Attraction of characteristic functions      298
Autoregression, autoregressive      419 421
Average time of return      574
Averages, moving      419 421 437
Axioms      138
Backward equation      117
Balance equation      420
Ballot Theorem      107
Banach space      261
Barriers      588 590
Bartlett’s estimator      444
Basis, orthonormal      267
Bayes’s formula      26
Bayes’s theorem      27 230
Bernoulli, distribution      155
Bernoulli, James      2
Bernoulli, law of large numbers      49
Bernoulli, random variable      34 46
Bernoulli, scheme      30 45 55 70
Bernstein, inequality      55
Bernstein, polynomials      54
Bernstein, proof of Weierstrass’ theorem      54
Bernstein, S.N.      4 307
Berry — Esseen theorem      63 374
Bessel’s inequality      264
Best estimator      42 69 see
Beta distribution      156
Bilateral exponential distribution      156
Binary expansion      131 394
Binomial distribution      17 155
Binomial distribution, negative      155
Binomial random variable      34
Birkhoff, G.D.      404
Birthday problem      15
Bochner — Khinchin theorem      viii 287 409
Borel — Cantelli lemma      255
Borel — Cantelli — Levy theorem      518
Borel, algebra      139
Borel, E.      4
Borel, function      170
Borel, rectangle      145
Borel, sets      143 147
Borel, space      229
Borel, zero-or-one law      380
Bose — Einstein      10
Boundary      536
Bounded variation      207
Branching process      115
Brownian motion      306
Buffon’s needle      224
Bunyakovskii, V.Ya.      38 192
Burkholder’s inequality      499
Canonical decomposition      544
Canonical probability space      247
Cantelli, F.P.      255 388
Cantor, G., diagonal process      319
Cantor, G., function      157 158
Caratheodory’s theorem      152
Carleman’s test      296
Cauchy Bunyakovskii inequality      38 192
Cauchy criterion for almost sure convergence      258
Cauchy criterion for convergence in mean-p      260
Cauchy criterion for convergence in probability      259
Cauchy, distribution      156 344
Cauchy, inequality      38
Cauchy, sequence      253
Central limit theorem      4 322 326 348
Central limit theorem for dependent variables      541
Central limit theorem, nonclassical condition for      337
Certain event      11 136
Cesaro limit      582
Change of variable in integral      196
Chapman, D.G.      116 248 566
Characteristic function of distribution      4 274
Characteristic function of random vector      275
Characteristic function of set      33
Charlier, C.V.L.      269
Chebyshev inequality      47 55 192
Chebyshev, P.L.      3 321
Chi, chi-squared distributions      156 243
Class $C^+$      515
Class convergence-determining      315
Class determining      315
Class monotonic      140
Class of states      570
Classical method      15
Classical models      17
Classification of states      569 573
Closed linear manifold      267
coin tossing      1 5 17 33 83 131
Coincidence problem      15
Collectively independent      36
Communicating states      570
Compact relatively      317
Compact sequentially      319
Compensator      482
Complement      11 136
Complete function space      260
Complete probability measure      154
Complete probability space      154
Completely nondeterministic      447
Conditional distribution      227
Conditional expectation in the wide sense      264 274
Conditional expectation with respect to $\sigma$-algebra      214
Conditional expectation with respect to decomposition      78
Conditional expectation with respect to event      220
Conditional expectation with respect to set of variables      81
Conditional probability      23 77 221
Conditional probability variance      83 214
Conditional probability with respect to a $\sigma$-algebra      212 214
Conditional probability with respect to a decomposition      77 212
Conditional probability with respect to a random variable      77 214
Conditional probability, regular      227
Conditional probability, Wiener process      307
Conditionally Gaussian      466
Confidence interval      74
Consistency Property      163 246
Consistent estimator      71 521 535
Construction of a process      245 246
Continuity theorem      322
Continuous at $\emptyset$      153 164
Continuous from above or below      134
Continuous time      177
Convergence of martingales and submartingales      508 515
Convergence of probability measures      Chap.III 308
Convergence of random variables: equivalences      252
Convergence of sequences      see Convergence of sequences
Convergence of sequences at points of continuity      253
Convergence of sequences in distribution      252 325 353
Convergence of sequences in general      310
Convergence of sequences in mean      252
Convergence of sequences in mean of order p      252
Convergence of sequences in mean square      252
Convergence of sequences in measure      252
Convergence of sequences in probability      252 348
Convergence of sequences with probability      252
Convergence of sequences, almost everywhere      252 353
Convergence of sequences, almost sure      252 353
Convergence of sequences, dominated      187
Convergence of sequences, monotone      186
Convergence of sequences, weak      309 311
Convergence of series      384
Convergence-determining class      315
Convolution      241 377
Coordinate method      247
Correlation, coefficient      41 234
Correlation, function      416
Correlation, maximal      244
Counting measure      233
Covariance      41 232 293
Covariance, function      306 416
Covariance, matrix      235
Cramer condition      400
Cramer transform      401
Cramer — Lundberg model      559
Cramer — Wold method      549
Cumulant      290
Curve of regression      238
Curvilinear boundary      536
Cyclic property      571
Cyclic subclasses      571
Cylinder set      146
d-system      142
Davis’s inequality      499
De Moivre — Laplace limit theorem      62
de Moivre, A.      2 49
Decomposition of martingale      507
Decomposition of probability measure      525
Decomposition of random sequence      447
Decomposition of set      12 292
Decomposition of submartingale      482
Decomposition, canonical      544
Decomposition, countable      140
Decomposition, Doob      482
Decomposition, Krickeberg      507
Decomposition, Lebesgue      525
Decomposition, of $\Omega$      12 140
Decomposition, trivial      80
Degenerate, distribution      298
Degenerate, distribution function      298
Degenerate, random variable      298
Delta function      298
Delta, Kronecker      268
Density of distribution      156
Density of measure with respect to a measure      196
Density of random variable      171
Density, Gaussian      66 156 161 238
Density, n-dimensional      161
Dependent random variables      103
Dependent random variables, central limit theorem for      541
Derivative, Radon — Nikodym      196
Detection of signal      462
Determining class      315
Deterministic      447
Deterministic, regularity      1
Dichotomy, Hajek — Feldman      533
Dichotomy, Kakutani      529
Difference of sets      11 136
Direct product      31 144 151
Dirichlet’s function      211
Discrete measure      155
Discrete random variable      171
Discrete time      177
Discrete uniform density      155
Discrete version of Ito’s formula      554
Disjoint      136
dispersion      41
Distance in variation      355 376
distribution      see also Distribution function Probability
Distribution function      34 35 152 171
Distribution function of functions of random variables      36 239ff.
Distribution function of sum      36 241
Distribution function, absolutely continuous      156
Distribution function, degenerate      288
Distribution function, discrete      155
Distribution function, finite-dimensional      246
Distribution function, generalized      158
Distribution function, n-dimensional      160
Distribution of objects in cells      8
Distribution of process      178
Distribution of sum      36
Distribution with density (list)      156
Distribution, Bernoulli      155
Distribution, Beta      156
Distribution, binomial      17 18 155
Distribution, Cauchy      156 344
Distribution, chi, chi-squared      243
Distribution, conditional      212
Distribution, discrete (list)      155
Distribution, discrete uniform      155
Distribution, entropy of      51
Distribution, ergodic      118
Distribution, exponential      156
Distribution, gamma      156
Distribution, Gaussian      66 156 161 293
Distribution, geometric      155
Distribution, hypergeometric      21
Distribution, infinitely divisible      341
Distribution, initial      112 565
Distribution, invariant      120
Distribution, limit      545
Distribution, lognormal      240
Distribution, multidimensional      160
Distribution, multinomial      20
Distribution, negative binomial      155
Distribution, normal      66 156
Distribution, Poisson      64 155
Distribution, polynomial      20
Distribution, probability      33
Distribution, stable      341
Distribution, stationary      120
Distribution, Student’s      155 244
Distribution, t-      155 244
Distribution, two-sided exponential      155
Distribution, uniform      156
Dominated convergence      187
Dominated sequence      496
Doob, J.L.      482 485 492
Doubling stakes      89 481
1 2 3 4
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