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 L´ 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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