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| Neuenschwander D. — Probabilities on the Heisenberg Group: Limit Theorems and Brownian Motion, Vol. 163 |
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| Предметный указатель |
Accompanying laws theorem 15 99
Accompanying system 99
Admissible mapping 15
Approximate martingale 6
Associated random measure 82
Atiyah — Singer theorems 2
Bernstein theorem 32
Braided group 6
Campbell — Hausdorff formula 9
Canonical coordinates 99
Capacity 22
Cartan subalgebra 29
Cauchy distribution 2
Central limit theorem 19 38 73 79
Compact group 98
Complete convergence 106
Composition of quadratic forms 9
Cone 26 27 56
Continuous convolution hemigroup 14 100 101
Continuous convolution semigroup 7 13 99 101
Contracting automorphism 17
Contracting automorphism group 40 41
Convergence of types theorem 19 20 39 90
Convolution operator 8
Cramer — Levy theorem 30
Descending central series 8
Diamond group 102
Dilatation 10 39 121
Discrete subgroup 98
Domain of attraction 16 40 41 86 87 89
Domain of normal attraction 16 37 86
Domain of partial attraction 16
Donsker invariance principle 6
Doob convergence theorem 122
Double point 73
Ergodic sequence 111
Euclidean motion group 98 102
Evolution equation 15
Exchangeable sequence 112
Exponential Lie group 11 13
Finite group 29
Free simply connected step 2-nilpotent Lie group 9
Freidlin — Ventsel theory 58 65
Full probability measure 38 88 89
Gateaux differential 66
Gaussian generating distribution 11
Gaussian measure 11 30 32 37 39 40 44 75 96 100
Gaussian random variable 11
Gaussian semigroup 11 29 30 38
Generating distribution 8
Generating distribution without Gaussian component 11
Generating family 15 101
Green function 50 72
Group of type H 9
Hausdorff measure 71
Heavy trimming 39
Heisenberg commutation relation 3
Heisenberg uncertainty principle 3
Hermitean hypergroup 98
Hilbert — Lie group 6
Holder inequality 36 106
Homogeneous dimension 10 57
Homogeneous norm 10
Hunt function 99
Hunt theory 22
Hypergroup 98
Infinitely divisible measure 12 13 97 99 101
Infinitesimal generator 8
Integration by parts for semimartingales 31
Intermediate trimming 39
Invariance group 39 88
Invariant set 111
Iwasawa decomposition 9
Jacobi identity 8
Killed Brownian motion 53
Killing rate 54
Killing set 53 54
Kochen — Stone Borel — Cantelli lemma 65
Kohn Laplacian 11 38
Kronecker lemma 102
L — S-full probability measure 20 38 86 112 115 118 120
Lagrangian multiplier 66
Laplacc operator 11
Law of large numbers for exchangeable sequences 112
Law of large numbers, Baum — Katz 106 109
Law of large numbers, Bose — Chandra 112
Law of large numbers, Erdos — Renyi 67
Law of large numbers, Hsu — Robbins — Erdos 106
Law of large numbers, Kolmogorov 74 84 95 101 106
Law of large numbers, Komlos 82
Law of large numbers, Marcinkiewicz — Zygmund 102 103 104 105 106 108 109
| Law of the iterated logarithm, Chover 112
Law of the iterated logarithm, Chung maximal 61
Law of the iterated logarithm, Hartman — Wintner 73
Law of the iterated logarithm, Levy asymptotic 58
Law of the iterated logarithm, Levy local 58
Lebesgue needle 56
Levy construction of first kind 89
Levy construction of second kind 89
Levy inequality 108
Levy measure 11
Levy stochastic area process 31 37
Levy — Hincin formula 11
Lie — Trotter product formula 13
Light trimming 39 89
Limit statute 82 105
Lindeberg theorem 17 33
Lipschitz continuous hemigroup 14 101
Ljapunov Theorem 35
Local centering 98 99
Location operator 3
Martingale 3 24 37 122
Maximal lemma 58 78
Maximum principle 22
Minkowski multiplication 6
Mixing sequence 6 112
Modulus trimming 39
moment 37 73 101 102 105 106 109
Momentum operator 3
Normal measure 31
Norming sequence 16 41 90
Occupation measure 72
Operator stable probability measure 13
Order statistics 88 89
Ottaviani inequality for homogeneous groups 113
Outlier resistance 39
p-adic group 6
Poincare criterion 27
Poisson approximation theorem 15
Poisson measure 7
Poisson semigroup 7 11 29
Polar coordinate decomposition 40 90
Positive graduation 10
Potential kernel 22
Primitive distribution 11 13
Prohorov distance 88
Prohorov theorem 42 99
Pseudo inner product 38
Pseudo-distance 45
Quantum group 6
Rate of convergence 73 106
Regular boundary 21
Right gradient 12
Robust statistics 39
Root set 12
Semigroup without Gaussian component 11 86 87 88 112 118 120
Semisimple Lie group 10 29
Semistable semigroup 13 29 31 121
Skew-symplectic mapping 38 86 87 120
Skorohod topology 37
Slowly varying function 87
Spectral decomposition 31
Stable semigroup 13 16 29 31 38 39 40 86 88 89 112 121
Standard Brownian motion 11 32 35
Statistics of directional data 1
Stirling formula 41
Stratified group 10
Strict domain of attraction 16 86
Strict domain of normal attraction 38 87 116
Strict domain of partial attraction 16
Strictly semistable semigroup 13 115 120 121
Strictly stable semigroup 13 38 86 112 116 118 121
Strictly universal law 16
Strongly root compact group 12
Sturm — Liouville equation 62
Subadditive process 24
Subsequence principle 82 105
Support function 6
Symmetric space 29 98
Symplectic form 38
Symplectic group 38
Symplectic mapping 38 86 87 120
Tauberian theorem 24
Three-series theorem 121 122
Trimmed product 40 89
Trimmed sum 39
Truncated random variable 44 91
Universal law 16 85 86
Wiener sausage 24 44
Wiener test 24
Zero-one law, Blumenthal 24 26
Zero-one law, Gallardo 24
Zero-one law, Kolmogorov 118 119 120
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