Taylor R.L. — Stochastic Convergence of Weighted Sums of Random Elements in Linear Spaces :: Электронная библиотека попечительского совета мехмата МГУ

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Taylor R.L. — Stochastic Convergence of Weighted Sums of Random Elements in Linear Spaces

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Название: Stochastic Convergence of Weighted Sums of Random Elements in Linear Spaces

Автор: Taylor R.L.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1978

Количество страниц: 216

Добавлена в каталог: 31.10.2008

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Предметный указатель

Banach space condition $G_\alpha$       97
Banach space convex of type (B)      86
Banach space, definition      9
Banach space, the space       10
Banach space, the space       11
Banach space, the space $L^\infty$       11
Banach space, the space c      10
Banach space, the space C[0,1]      10
Banach space, type p      102
Beck and Giesy's Strong Law of Large Numbers      82—83
Beck's Strong Law of Large Numbers for B-convex spaces      86—96
Bochner integral      39
Borel function      12
Borel subsets      12
Borel subsets in D[0,1]      161
Completeness      7
Consistent decision procedure      191
Consistent decision procedure consistent with convergence in probability      191
Convergence comparisons      29
Convergence complete      67
Convergence in D[0,1]      154—165
Convergence in mean      28
Convergence in probability      28
Convergence of series      105
Convergence of series of random elements in $G_\alpha$ spaces      99—100
Convergence of stochastic process      186—190
Convergence of weighted sums of random elements      108—145
Convergence of weighted sums of random variables      63—70
Convergence with probability one      28
Convergence, almost surely      28
Convergence, rates of      105
Convexity      also see Geometric Conditions
Convexity and tightness in D[0,1]      166 179—184
Convexity, convex of type (B)      86
Convexity, discussion of      86—875
Convexity, lack of convexity in D[0,1]      158
Convexity, uniformly convex      86
Determining class      31 see
Dual space in characterizing identical distributions and independence      32—33
Dual space in the convergence of weighted sums      110—111
Dual space in the laws of large numbers      75—80
Dual space of a linear topological space      8
D[0,1], basic properties      154—159
D[0,1], characterization of compactness      158
D[0,1], Daffer and Taylor’s SLLN’s      175—179
D[0,1], expected values      159
D[0,1], general introduction      4
D[0,1], Ranga Rao’s SLLN      172—174
D[0,1], topology of the Skorohod metric      154—155
D[0,1], uniform topology      154—155
Family of unicity, definition      31
Family of unicity, examples      31—32
Frechet space, convergence of weighted sums      136
Frechet space, definition      9
Frechet space, laws of large numbers      104—106
Frechet space, the space $C[0,\infty]$       11
Frechet space, the space F      11
Frechet space, the space s      9
Generalized Gaussian random variables      66
Geometric conditions convergence of weighted sums      137—145
Geometric conditions convex of type (B)      86
Geometric conditions, $G_\alpha$ condition      97
Geometric conditions, the strong law of large numbers      96—104
Geometric conditions, type p      102—103
Hahn — Banach theorem      13
Hahn — Banach Theorem, use of      27 94
Hilbert space coordinate uncorrelation      61
Hilbert space laws of large numbers      49—54
Hilbert space, definition      9
Hilbert space, the space       11
Hoffmann — Jorgensen and Pisier’s Strong Law of Large Numbers      102—103
Identical Distributions and transformations      30—31
Identical Distributions characterized by finite—dimensional distributions      34
Identical Distributions characterized by the dual space      32
Identical Distributions, definition      30
Independence characterized by finite-dimensional distributions      36
Independence characterized by the dual space      32—33
Independence moment conditions in $G_\alpha$ spaces      97—98
Independence, definition      30
Inner product in defining uncorrelation      50
Inner product, definition      9
Isometry and Isometric      13
Isomorphism and Isomorphic      13
Ito and Nisio’s convergence of series      105
Kronecker’s lemma      101
Laws of Large Numbers and Geometric conditions      96—104
Laws of Large Numbers in a separable Hilbert space      51—54
Laws of Large Numbers in decision theory applications      190—193
Laws of Large Numbers in Frechet spaces      104—106
Laws of Large Numbers in separable normed linear spaces      71—104
Laws of Large Numbers in type p spaces      102—103
Laws of Large Numbers, Beck and Giesy’s SLLNs      82—83
Laws of Large Numbers, Beck and Warren’s SLLN      80
Laws of Large Numbers, Beck’s SLLN and convexity      86—96
Laws of Large Numbers, convergence of weighted sums      3
Laws of Large Numbers, counterexample in       80—81
Laws of Large Numbers, counterexample in       95
Laws of Large Numbers, estimation applications      197—201
Laws of Large Numbers, general discussion      3
Laws of Large Numbers, Hoffman — Jorgensen and Pisier’s SLLN      102—103

Laws of Large Numbers, Monte Carlo methods      196—197
Laws of Large Numbers, Mourier’s SLLN      72—74
Laws of Large Numbers, SLLN for tight random elements      133
Laws of Large Numbers, SLLNs in D[0,1]      172—179
Laws of Large Numbers, strong laws for random variables      46—48
Laws of Large Numbers, weak law for random variables      43
Laws of Large Numbers, WLLN for tight random elements      129
Laws of Large Numbers, WLLNs in D[0,1]      166—170
Linear Space, definition      6
Linear Space, the linear space D[0,1]      157
Linear topological space      8
Markov’s inequality      29
Measurability Borel      12
Measurability problem      1
Measurability strongly      23
Metric space D[0,1]      157
Metric space, definition      7
Metric space, linear      8
Mourier’s Strong Law of Large Numbers      72—74
Norm definition      8
Norm, normed linear space      8
Norm, of a continuous linear functional      13
Norm, uniform norm for D[0,1]      15
Orthogonal, definition      18
Orthogonal, orthonormal      18
Orthogonal, weakly orthogonal      80
Pettis integral as an expected value      38
Pettis integral, existence of      40—41
Pettis integral, properties of      38—39
Random element(s) in $G_\alpha$ spaces      97—104
Random element(s) in       21
Random element(s) in a separable Hilbert space      4
Random element(s) in a separable semimetric space      25—26
Random element(s) in D[0,1]      159—165
Random element(s) in R      21
Random element(s), addition of      28
Random element(s), characterized by a Schauder basis      24
Random element(s), characterized by the dual space      27—28
Random element(s), convergence of weighted sums      108—152
Random element(s), countably-valued      22—23
Random element(s), definition      21
Random element(s), expected value of      38 see
Random element(s), identically distributed      30
Random element(s), independent      30
Random element(s), laws of large numbers for      51—54 71—104
Random element(s), limits of      22—23
Random element(s), probabilistic convergence      26
Random element(s), product with a random variable      24
Random element(s), strongly-measurable      23
Random element(s), transformations of      22
Random element(s), type (A)      88
Random element(s), uncorrelated      50
Random element(s), variance of      3 8
Schauder basis characterizing compactness      19
Schauder basis characterizing random elements      24
Schauder basis characterizing the expected value      42
Schauder basis characterizing weakly uncorrelated      56
Schauder basis coordinate functionals      14
Schauder basis coordinate uncorrelation      55
Schauder basis in convergence of weighted sums      112—127
Schauder basis in obtaining laws of large numbers      72—75
Schauder basis partial sum operators      15
Schauder basis, definition      14
Schauder basis, examples      15—18
Schauder basis, monotone      14
Semimetric space      7
Seminorm      8
Separability and random elements      23
Separability stochastic processes      2
Separability, definition      9
Skorohod metric      154
Stochastic Processes and random elements      1
Stochastic Processes stationary increments and identically distributed random elements      35
Stochastic Processes, Brownian motion processes      36
Stochastic Processes, laws of large numbers for      84 186—190
Stochastic Processes, Poisson processes      36
Taylor and Padgett’s Strong Law of Large Numbers      83—84
Taylor’s Weak Laws of Large Numbers      75—79 85
Tightness centering random elements      121
Tightness convergence of weighted sums of random elements      124—134
Tightness for Brownian motion processes      187
Tightness, convex tightness in D[0,1]      166
Tightness, definition      120
Toeplitz sequence      63 109
Uncorrelation and independence      52
Uncorrelation comparisons      55—63
Uncorrelation in a separable Hilbert space      5
Uncorrelation pointwise in D[0,1]      169
Uncorrelation random variables      45
Uncorrelation, coordinate uncorrelated      55
Uncorrelation, weakly uncorrelated      55
Weighted Sums, applications in quality control      195—196
Weighted Sums, convergence and tightness      120—136
Weighted Sums, convergence for random elements      108—152
Weighted Sums, convergence for random variables      63—73
Weighted Sums, convergence of randomly weighted sums      146—151
Weighted Sums, general appearance      2
Weighted Sums, geometric conditions and convergence      137—145
Weighted Sums, random weighting      4
Woycznski’s Strong Law of Large Numbers      101—102

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