SKIFF
发表于 2025-3-25 06:08:14
An Arbitrary Space of Elementary Events,ecessarily countable. The concepts of algebra and sigma-algebra of sets are introduced and discussed in detail. Then the axioms of probability and, more generally, measure are presented and illustrated by several fundamental examples of measure spaces. The idea of extension of a measure is discussed
英寸
发表于 2025-3-25 10:56:03
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记忆法
发表于 2025-3-25 15:19:11
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allergy
发表于 2025-3-25 17:24:09
Sequences of Independent Trials with Two Outcomes,nomial probabilities is proved in Sect. . using Stirling’s formula (covering both the normal approximation zone and the large deviations zone). The same section also contains a refinement of that result, including a bound for the relative error of the approximation, and an extension of the local lim
Fecundity
发表于 2025-3-25 20:18:32
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小步舞
发表于 2025-3-26 00:49:46
Characteristic Functions,ated to the nature of the underlying distributions. Section . presents the proofs of the inversion formulas for both densities and distribution functions, and also in the space of square integrable functions. Then the fundamental continuity theorem relating pointwise convergence of characteristic fu
Ovulation
发表于 2025-3-26 07:08:58
Sequences of Independent Random Variables. Limit Theorems,ntically distributed summands, both using the apparatus of characteristic functions. Section . establishes general conditions for the Weak Law of Large Numbers for general sequences of independent random variables and also conditions for the respective convergence in mean. Section . presents the Cen
outer-ear
发表于 2025-3-26 10:15:57
Large Deviation Probabilities for Sums of Independent Random Variables,n probabilities, Cramér’s condition is introduced and the main properties of the Cramér and Laplace transforms are discussed in Sect. .. A separate subsection is devoted to an in-depth analysis of the key properties of the large deviation rate function, followed by Sect. . establishing the fundament
横截,横断
发表于 2025-3-26 16:06:37
Renewal Processes,ishes the basic terminology and proves the integral renewal theorem in the case of non-identically distributed random variables. The classical Key Renewal Theorem in the arithmetic case is proved in Sect. ., including its extension to the case where random variables can assume negative values. The l
责难
发表于 2025-3-26 19:08:34
Properties of the Trajectories of Random Walks. Zero-One Laws,e concepts of lower and upper functions are introduced. Section . contains the first Kolmogorov inequality and several theorems on convergence of random series. Section . presents Kolmogorov’s Strong Law of Large Numbers and Wald’s identity for stopping times. Sections . and . are devoted to the Str