Index
absolutely continuous, 237
almost everywhere, 77
convergence, 78
almost surely, 110
arc sine law, 26
Azuma’s inequality, 232
Bayes’s formula, 28
Bernoulli measure, 33
Bernstein polynomial, 132
Berry–Esseen theorem, 142
biased random walk, 35
binomial, 11
coefficient, 11
N choose m, 11
distribution
parameters (n, p), 34
Borel
measurable function, 56
measurable set, 56
measure, 57
Borel–Cantelli lemma, 32, 244
branching process, 178
extinction, 178
Brownian motion, 206
Feynman–Kac formula, 269
evy’s characterization, 263
relative to {Ft : t 0}, 210
scaling property, 209
strong law, 213
time inversion invariance, 213
centered Gaussian family, 152
central limit theorem, 140
De Moivre’s, 18
Lindeberg’s, 137
Chapman–Kolmogorov equation, 194
Chebychev’s inequality, 44
complement, 4
concave function, 85
conditional expectation, 110
conditional probability, 27
contraction, 171
convergence
μ-almost everywhere, 78
in μ-measure, 79
convex
function, 85
set, 84
convolution, 121
countably additive, 57
covariance, 143
cumulant of a random variable, 51
De Morgan’s law, 6
decreasing events, 5
density of a distribution, 117
difference, 4
discrete arcsine measure, 33
disjoint sets, 4
distribution, 59
having density, 117
of a random variable, 32
of a stochastic process, 193
distribution function, 70
Doeblin’s
281
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