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| Adler R.J. — An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes |
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| Предметный указатель |
 processes 36
 136
 space of a Gaussian process 69 142
 -radial processes 37
Adler vi 26 33 35 39 58 118 127 130 131 132 136 139 145 147
Albin vi 119
Aldous 118
Anderson 88 116
Approximate continuity 113
Approximate growth functions 113 116
Banach space applications 59
Banach space valued processes 35 44
Bass 39
Bassan 132
Belyaev’s dichotomy 73
Berman 49 121
Borell 43.
Borell’s inequality 42 43 49 60 62 117 119 123
Boundedness 80 85
Boundedness and continuity see “Continuity”
Brown vi 57 58 130 132 136 139
Brownian motion 6 59 68 76
Brownian sheet 7 29 39 40 78
Brownian sheet, pinned 8 119 129 131 132
Brownian sheet, set-indexed 27
Brunn — Minkowski inequality 43
Cabana 132
Cairoli 7
Cambanis 73
Canonical metric 3
Cervonenkis 29 130
Continuity 3 13 63 85
Continuity and boundedness 62 85 106
Continuity and entropy 4 106 107 114
Continuity and majorising measures 80
Continuity and orthonormal expansions 71
Continuity at a point 66
Convex sets 11
Cosine process 131 139
Covariance function 2
Covariation function 58
Cramer 15
Dalang 7
Dawson v
Diameter 4
Dichotomies 73
Differential structure of sample paths 147
Diffusions 58 61
Discontinuous processes 9 15 29 112
Dobric 126
Dobrushin 26
Dudley v vi 4 8 11 28 29 30 32 115
Dudley sets 28
Dvoretzky 61
Dynkin 26 42 142 144 145
Elliptically contoured distributions 54 55
Ellis 55
Empirical measures 8
Empirical processes 8 148
entropy 1 4 13ff 41 104ff
Entropy, two-parameter 109 146
Evans 111
Expansions of Gaussian processes, Karhunen — Loeve 69 75 79
Expansions of Gaussian processes, orthonormal 17 70
Expansions of Gaussian processes, Talagrand 18 40
Extremal theory 131 146
Feigin 39
Feldman, (Epstein) vi 26 145
Feller 134
Femique v vi 1 36 37 38 53 58б 77 80 81 88 106.
Fourier series 16
Free field 26
Garsia 80
Gaussian processes 1ff
Gaussian variables 1
Geman 112 114
Generalised processes 19
Gine 88 116
Goodman 132
Gordon 57 61
Gordon’s inequality 55 61
Green’s function 143
Haar measure 83
Hahn 88
Hausdorff dimension 34
Hogan 186
Incremental variance 13 122
Index  processes 34
Infinite dimensional processes 26
Infinitely divisible processes 57
Iscoe 36
Isomorphism of Banach spaces 59
Isomorphism theorem 42 144
Ito 26 71
Ito’s formula 43 46 61
JAIN vi 53 73
Joag-Dev 48 55
Kac 138
Kahane 55
Kallianpur 73
| Karatzas 45 46
Karhunen — Loeve expansion 75ff
Kiefer 138
Kolmogorov 25 41
Kolmogorov — Smirnov tests 9 58 131 132 136
Landau 43
Leadbetter 15 33 118 147
Leap-frog 117
Ledoux 44
Linde 58 59
Lindgren v 33 118 147
Lower layers 9
lu 58 136 139
Major 142
Majorising measures 1 80ff 114 145
Majorising measures and entropy 105
Majorising measures, discrete 111
Mandelbaum 142
Marcus vi 16 17 18 36 37 39 43 53 126 145
Markov processes 26 133 142 144
Martingale 45
Maurey 43
McDonald 36
Mercer’s theorem 75
Mesure majorante see “Majorising measures”
Metric entropy see “Entropy”
Milman 59
Modulus of continuity 5 64 66 87 115
Nisio 71
Non-Gaussian processes 36
Ornstein — Uhlenbeck process 78 101
Orsingher 132
Oscillation function 72
Ossiander 88 116
Perlman 48 55
Pickands 118
Pisier vi 16 17 18 37 39 43 44 59 61
Piterbarg vi 131
Pitt 48 55.
Plackett 48
Poisson clumping heuristic 118
Poisson limit theorems 99 147
Pollard 8 82 104
Preston 1 80
Pseudo-metric 3
Pyke 9 39 135
Rajput 73
Random fields 19 132 147
Reproducing kernel Hilbert space 66
Riesz 75
Rinott 55
Rodemich 80
Rootzen v 33 118 147
Rosen 145
Rumsey 80
Samorodnitsky vi 12 19 38 58 108 121 127 130 131
Schechtman 59
Schwartz space 25
Separability 2
Set-indexed processes 27 148
Shepp 43
Shreve 45 46
Siegmund 186
Slepian 48 140
Slepian’s inequality 36 42 48ff 132 136
Slepian’s inequality, failure of 54
Slepian’s inequality, variations on 54ff
Spectral measure 15 38 58
Spectrum 15
Stable processes 38 58
Stationary processes 15 83 128
Sudakov 4 106
Sudakov inequality 106 116
Sudakov — Fernique inequality 53 91 95
Suprema 5 9 117ff
Suprema, exponential moments 63
Suprema, position of 81 104
suprema, tail distributions 117ff 135
Sz-Nagy 75
Talagrand v vi 1 18 36 39 63 80 81 85 86 118 121
Taqqu 38
Tihomirov 25 41
Total boundedness 4
Ultrametricity 110
Vapnik 29 30
Vapnik — Cervonenkis classes 29
Vector-valued processes 32
Walsh 7
Watanabe 26
Weber 119 126
Weron 138
White noise 6 7 31
Wife 146
Wolfowitz 138
Wong 7
Wschebor 132
Zaanen 75
Zakai 7
Zero-one law 66 73
Zinn 36 88 114 126 145
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