Ash R.B., Doléans-Dade C.A. — Probability and Measure Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Ash R.B., Doléans-Dade C.A. — Probability and Measure Theory

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Название: Probability and Measure Theory

Авторы: Ash R.B., Doléans-Dade C.A.

Аннотация:

Probability and Measure Theory, Second Edition, is a text for a graduate-level course in probability that includes essential background topics in analysis. It provides extensive coverage of conditional probability and expectation, strong laws of large numbers, martingale theory, the central limit theorem, ergodic theory, and Brownian motion.

- Clear, readable style
- Solutions to many problems presented in text
- Solutions manual for instructors
- Material new to the second edition on ergodic theory, Brownian motion, and convergence theorems used in statistics
- No knowledge of general topology required, just basic analysis and metric spaces
- Efficient organization

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second edition

Год издания: 2000

Количество страниц: 516

Добавлена в каталог: 20.03.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Probability measure, induced by a random variable      173
Probability measure, induced by a random vector      176
Probability space      5
Product $\sigma$ -field      102
Product measure theorem      102 105 109 111 112
Product of $\sigma$ -fields      114
Product of measures      111 116
Progressively measurable process      431
Projection      134 144
Projection of a probability measure      118
Projection theorem      135
Prokhorov's theorem      302 340
Pseudometric      87
Pythagorean relation      132
Quadratic variation of Brownian motion paths      409-410
Queueing process      287
Rademacher functions      248
Radon - Nikodym derivative      68
Radon - Nikodym theorem      65 95
Random object      178
Random signs problem      239 281
Random variable      173
Random vector      176
Random walk      200 438
rectangle      113 117
Recurrent states      285 288 438-439
Recurrent transformation      355
Reflexive space      157
Regular conditional distribution function      229
Regular conditional probability      231
Relatively compact family of finite measures      301
Reverse martingales (submartingales, supermartingales)      248
Riemann - Stieltjes integral      58-59
Riemann integral      55-59
Riemann zeta function      328
Riesz lemma      150
Riesz representation theorem      144 147
Right-continuous family of sigma-fields      415
Right-continuous function      22 336
Right-semiclosed intervals      4 29
Rotations of the circle      346 353
Sample space      166
Section      102
Semicontinuous functions      122 441
Seminorm      87 127
Separable Hilbert spaces      138
Set function      3
Shannon - McMillan theorem      384
Shifts      346
Signed measure      62
Simple function      37
Simple random variable      174
Singular measure      60 68
Skorokhod's theorem (Skorokhod construction)      334
Slutsky's theorem      332
Solvability theorem      165
Space spanned by a subset of a normed linear space      135
Stable distributions      317-320
Standard deviation      191
State space      196
Stationary probability measure      347 353
Stationary sequence of random variables      347 353

Steinhaus' lemma      44
Stochastic matrix      196
Stochastic process      399
Stopping time      270 414
Strong convergence      159
Strong Law of Large Numbers      200 242 278
Strong Markov property      416
Subadditivity      127 153
Sublinear functional      153
Submartingale and supermartingale inequalities      308
Submartingales      248ff. 420
subspace      133
Summation by parts      236
Sup norm      129 143
Supermartingales      248ff. 420
Symmetric events      245
Symmetrization      281
Tail $\sigma$ -field      244
Tail events      244
Tail functions      244
Theorem of total expectation      209
Theorem of total probability      172 209
Tight family of finite measures      301
Time average      349
Toeplitz lemma      236
Topological vector space      128
Total variation      62
Transient states      285 438-440
Transition matrix      198
Transition probabilities      198
Translation-invariant measures      34 35
Translations      346 353
Triangular array      321
Truncation inequality      303
Two-sided exponential density      176
Two-sided shifts      143 346 353
Types, convergence of      314
Uncertainty      376
Uniform asymptotic neglibility (uan)      313
Uniform convergence in the central limit theorem      329
Uniform convergence of linear operators      148
Uniform density      175
Uniform integrability      262 266ff.
Uniformly bounded random variables      308
Upcrossing theorem      258 277
Upper limit      2
Upper semicontinuous (USC) functions      122 441
Upper variation      62
Vague convergence of measures      see Weak convergence of measures
Variance      191
Variation of a function      74
Variation of Brownian motion paths      409
Version of a process      400
Vitali - Hahn - Saks theorem      44
Wald's Theorem      277
Wandering set      355
Weak compactness theorem      300ff.
Weak convergence in a normed linear space      159
Weak convergence of distribution functions      125 290
Weak convergence of measures      124 290 338 339
Weak law of laige numbers      198
Zero-one laws      244-246

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