Durrett 释义 [人名] 达雷特
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7161 6 1:11:36 App 高等概率论讲解~ durrett概率论2.3 Borel-Cantelli引理 836 2 33:28 App 高等概率论讲解~durrett概率论2.4强大数定律(2) 446 -- 1:42:38 App 测度积分与概率(高等概率论)第9讲:独立性,收敛与积分基础 313 3 1:41:14 App 高等概率论第10讲-积分变换 533 -- 33:08 App ...
Durrett在他的《概率论》中证明了一个关于条件期望的Jensen不等式: 设φ 是下凸函数,则 φ(E(X|G))≤E(φ(X)|G) 证明如下:如果 φ 是线性的,那么命题显然。 下设φ 非线性,令 S={(a,b):a,b∈Q,ax+b≤φ(x),∀x∈R} 则φ(x)=sup(a,b)∈S{ax+b} ,从而 E(φ(X)|G)≥E(aX...
\begin{split} &\lambda\left(A\right)+\varepsilon<\inf\left\{\left.\lambda\left(O\right)\right|A\subset O\wedge O\text{ open}\right\}\\ &<\lambda\left(O\right)\leq\sum_{n\in\mathbb{N}^*}\lambda\left(O_n\right)<\lambda\left(O\right)\leq\sum_{n\in\mathbb{N}^*}\left...
Then for any x_{0}\in\mathbb{R}, if that \liminf_{y\rightarrow x_{0}}f\left(y\right)< f\left(x_{0}\right), denote a_{0} and \left(x_{i}\right)_{i\in\mathbb{N}^{*}}\rightarrow x_{0} such that \liminf_{y\rightarrow x_{0}}f\left(y\right)<a_{0}<f\left(...
Let Ω=R , F= all subsets so that A or Ac is countable, P(A)=0 in first case and =1 in the second. Show that (Ω,F,P) is a probability space. Proof We'll first show that (Ω,F) is a σ-field. Denote that F=F1∪F2 , in which F1={A∈Ω:A is countable} and F2=...
durrett的概率论 Durrett的概率论是概率论的一大分支,主要讨论事件发生的可能性。它的研究对象是随机事件,即不能预测其结果的事件。在Durrett的概率论中,事件的可能性可以通过统计方法来计算,通常使用频率公式和主观概率公式。©2022 Baidu |由 百度智能云 提供计算服务 | 使用百度前必读 | 文库协议 | 网站地图 |...
\begin{split} &0\leq \mathbb{P}\left(g\left(X\right)\leq y\right)=\mathbb{P}\left(X\leq g^{-1}\left(y\right)\right)\\ &\leq\mathbb{P}\left(X\leq g^{-1}\left(g\left(\alpha\right)\right)\right)= \mathbb{P}\left(X\leq \alpha\right)=0\\ \end{split} thus \mathbb...
A.1.1 Give a example of two probability measures \mu eq u on \mathcal{F}= all subsets of \left\{1,2,3,4\right\} that agree on a coleection of sets \mathcal{C} with \sigma\left(\mathcal{C}\right)=\ma…