Gray R.M. — Probability, Random Processes and Ergodic Properties :: Электронная библиотека попечительского совета мехмата МГУ

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Gray R.M. — Probability, Random Processes and Ergodic Properties

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Название: Probability, Random Processes and Ergodic Properties

Автор: Gray R.M.

Язык:

Рубрика: Математика/Вероятность/Стохастические процессы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 209

Добавлена в каталог: 24.10.2004

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

Предметный указатель

$F_\sigma$ set      51
$G_\delta$       51
$G_\delta$ set      51
norm      85
$\bar{\rho}$ -distance      180
$\mathcal{Z_+}$       10
$\mathcal{Z}$       10
$\sigma$ -field      5
Absolutely continuous      105 107
Addition      10 36
Additive      7
Additive, finitely      7
Affine      192 195
Almost everywhere      74 83 84
Almost everywhere ergodic theorem      153
Almost surely      84
Alphabet      5 8 65 66
AMS      131
AMS, block      158
Analytic space      25
Arithmetic mean      82
Asymoptotic mean expectation      142
Asymoptotically dominates      134
Asymoptotically generate      29
Asymoptotically generates      27
Asymptotic mean stationary      123
Asymptotically mean ststionary      93 131
atom      26
Autocorrelarion      82
Average      65
Bad atoms      32
Ball, open      49
Banach space      53
Barycenter      187 192
Base      50
Basis      28 29
Binary indexed      27
Birkhoff ergodic theorem      153
Block AMS      158
Block stationary      131
Borel field      43 50
Borel space      25 49
Borel — Cantelli lemma      86
Canonical binary sequence function      28
Cantor's intersection theorem      53
Caratheodory      17 22 26 41 42 177
Cartesian product      37
Cartesian product space      13
Carving      57
Cauchy sequence      53
Cauchy — Schwarz inequality      76
Cearo mean      82
Chain rule      80
Change of variables      80
Circular distance      35
Class, separating      30
Code      23
Complete metric space      53
Compressed      139
Conditional expectation      102
Conservative      140
Consistent      41
Continuity at $\emptyset$       7
Continuity from above      7
Continuity from below      7
continuous      178
Continuous function      52
Converge in mean square      85
Converge in quadratic mean      85
Converge weakly      179
Convergence      38 84
Convergence in probability      84
Convergence with probability one      84
Convergence,       85
Convergence,       85
Coordinate function      82
Countable extension property      26 40
Countable subadditivity      18
Countably generated      26
Cover      18
Cylinders, thin      34
De Morgan's laws      6
Dense      52
Diagonal sequence      38
Diagonalization      38
Diameter      50
Digit measurement      66
Directly given random process      15
Discrete time random process      10
Distance      35
Distance $\bar{\rho}$       180
Distance, circular      35
Distance, distributional      175
Distance, Hamming      35
Distance, Levenshtein      36
Distance, rho-bar      180
Distance, shtein      180
Distance, stein      180
distribution      8 14
Distributional distance      175
Dominated Convergence Theorem      78
Dynamical system      11
Dynamical system, recurrent      138
Ensemble average      66
Equivalent      107
Equivalent metrics      50
Equivalent random processes      15
Ergodic      147
Ergodic components      190
Ergodic decomposition      160 161 187 198
Ergodic properties      123 146
Ergodic property      124
Ergodic theorem      65
Ergodic theorem, subadditive      164
Ergodic theory      11
Ergodic, totally      159
Ergodicity      146
Euclidean norm      37
Euclidean space      36 54
Event recurrent      138
Event space      5
Events input      8
Expectation      66
Expectation, conditional      102
Extended Fatou's lemma      78
Extended monotone convergence theorem      77
Extension of probability measures      25
Extension theorem      41
Fatou's lemma      78
Field      6
Field, standard      29 40
Fields increasing      27
Finite additivity      7
Finite intersection property      29
Finitely additive      7
Function, continuous      52
Function, tail      136
Generated $\sigma$ -field      160
Good sets priciple      32
Good sets principle      14 26
Hamming distance      35
Hilbert space      53 102
I.o.      133
IID      149
Incompressible      140
Increasing fields      27
Independent      117
Independent and identically disributed      149
Indicator function      9 28
Infinitely recurrent      140

Inner product      85
Inner product space      37 85
Input events      8
Integer sequence space      34 55 57
Integrable      74
integral      74
Integrating to the limit      77
Intersection sets      27
Invariant      91 132
Invariant function      125
Invariant measure      125
Invariant, totally      133
Isomorphic dynamical systems      24
Isomorphic measurable spaces      23
Isomorphic probability spaces      23
Isomorphism      23
Iterated expectation      114
Join      66
Kernel      59
Kolmogorov Extension Theorem      41
Kroneker $\delta$ function      35
l.i.m.      85
Lag      82
Lebesgue decomposition theorem      107
Lebesgue measure      43 47
Lee metric      35
Left shift      11
Levenshtein distance      36
Limit in the mean      85
Limit inferior      70
Limit infimum      70 71
Limit point      50
Limit superior      70
Limit supremum      70
Limiting time average      83
Lower limit      70
Lusin space      25
Maesurability      11
Maesurable      19
Maesure      7
Maesurement      65
Markov chain      37 119 182
Markov inequality      76
Markov k-step      190
Markov kth order      190
Markov property      119
Martingale      118
Match      35
Maximal ergodic lemma of theorem      153
Mean      66
Measurable function      8 96
Measurable scheme      59
Measurable space      5
Measurable space, standard      29 40
Measure spase      7
Measure, Lebesgue      43 47
Measurement, digital      66
Measurement, discrete      66
Memoryless      149
Metric      35
Metric space      35
Metric, Hamming      35
Metric, Lee      35
Metrically transitive      147
Metrics, equivalent      50
Mixing      149
Mixture      9 160 173
Monotone class      6 16 17 22
Monotone Convergence Theorem      77
Monotonicity      18
Multiplication      36
N-ergodic      150
Nested expectation      114
Nonsingular      140
Norm      85
Norm, Euclidean      37
Normed linear spase      36
Null preserving      140
One-sided random process      10
Open ball      49
Open set      49
Open sphere      49
Orthogonal      103
Outer measure      19
Parallelogram law      102
Partition      27
Partition distance      38
Perpendicular complement      103
Point      35
Points, generetic      160
Pointwise ergodic theorem      153
Polish Borel space      54
Polish space      54 88
Power set      6 24 34
Pre-Hilbert space      37
Probabilistic average      66
Probability space      5 6
Probability space, associated      16
Process, asymptotically mean stationary      131
Product distribution      119
Product space      13 37
Product, cartesion      37
Prohorov distance      185
Projection      102 104
Projection theorem      104
Pseudo-metric      35
Quantization      68
Quantizer      61 69
Radon space      25
Radon — Nikodym derivative      105
Radon — Nikodym therem      105
Random process      10
Random process, directly given      15
Random process, discrete time      10
Random process, one-sided      10
Random process, two-sided      10
Random processes, equivalent      15
Random variable      5 8
Random variable, discrete      66
Random vector      10
Reccurent      138
rectangle      13
Recurrence      138
Recurrent dynamical system      138
Recurrent event      138
Regular conditional probability      95
Remote $\sigma$ -field      136
Restriction      99
Rho-bar distance      180
Sample average      81 — 83
Sample mean      82
scalar      36
Scheme      58 59
Scheme, measurable      59
Schemes      58
Seminorm      37
Separable      52
Separating class      30
Sequentially compact      38
Set, $F_\sigma$       51
Set, $G_\delta$       51
Set, open      49
Shift      11 81
Shift transformation      11
Shtein distance      180
Sigma-field      5
Simple function      66
singular      107
SIZE      35
Smallest $\sigma$ -field      13

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