此时,停时的期望值为 \begin{align} \mathbb{E}[N_{t}] &= \sum_{n = 1}^{\infty}\int_{0}^{t} I(x) dx \\ &= \sum_{n = 1}^{\infty} \frac{t^n}{n!} \\ &= e^{t} - 1 \end{align} 从这里也可以很容易看出来,如果让 n 个均匀分布在 (0,1) 上的随机数相加直
设X={Xt,t≥0}为布朗运动且是标准马氏过程,Nt=σ(Xs,s≤t),τ为{Nt}停时. 若对有x∈R,有Exτ<∞,则 且ExX(τ)=x,且Ex|Xτ−x|2=Exτ. 证明 因为与{Xt,Nt}与{Xt2−t,Nt}为Px鞅.0≤τ∧t≤t,对0,τ∧t用有界停时定理得 ExX(t∧τ)=ExX(0)=x,(1)ExX2(t∧τ)−Ex(t∧...
所以构造一个鞅是可能的,同时因为大部分时候对于一个停时TT,都有E[T]<∞E[T]<∞,所以如果能构造出一个合适的鞅(即满足定理1.2.31.2.3的第三个条件),就可以通过定理1.2.31.2.3来计算一些从初态X0X0到终态XTXT过程中事件集合非常之巨大的问题
课件-概率论中的条件期望与停时 Conditionalityandstoppingtimesinprobability MarkOsegard,BenSpeidel,MeganSilberhorn,andDickensNyabuti 1 ConditionalExpectation 2 ConditionalProbability Discrete:ConditionalProbabilityMassFunction PXx|YyPXx,YyPYy Continuous:ConditionalProbabilityDensityFunction f(x,y)fX|Y(x|y):fX(y)...
1. 一类概率期望问题的杀器:势函数和鞅的停时定理(4424) 2. CEOI2019 / CodeForces 1192B. Dynamic Diameter(2667) 3. 学习总结:斯特林数( Stirling number )(2244) 4. 多项式牛顿迭代法(1061) 5. 一类匹配问题的移位技巧(The SHIFT Trick)(853) 评论排行榜 1. 一类概率期望问题的杀器:势函数和...
概率论7期望方差中心极限课件.ppt 热度: 概率论与数理统计数学期望ex分析解析ppt课件 热度: 相关推荐 Conditionalityand stoppingtimesin probability 1 ConditionalExpectation 2 ConditionalProbability Discrete:ConditionalProbabilityMassFunction yYP yYxXP , yYxXP| Continuous:ConditionalProbabilityDensityFunction )( )...
课件-概率论中的条件期望与停时-50页文档 Conditionalityandstoppingtimesinprobability MarkOsegard,BenSpeidel,MeganSilberhorn,andDickensNyabuti ConditionalExpectation ConditionalProbability Discrete:ConditionalProbabilityMassFunction PXx|YyPXx,YyPYy Continuous:...
概率论中条件期望和停时.ppt,Wald’s Proof… By the Strong Law of Large Numbers, Wald’s Proof… Also Concluding So as we let Which can be manipulated into our preposition: Miners Problem Sample Conditional and Stopping times in probability problem The pro
课件-概率论中的条件期望与停时 Conditionalityandstoppingtimesinprobability MarkOsegard,BenSpeidel,MeganSilberhorn,andDickensNyabuti 1 ConditionalExpectation 2 ConditionalProbability Discrete:ConditionalProbabilityMassFunction PXx|YyPXx,YyPYy Continuous:ConditionalProbabilityDensityFunction fX|Y(x|y):f(x,y)fX(y)...
1、Conditionality and stopping times in probability,Mark Osegard, Ben Speidel, Megan Silberhorn, and Dickens Nyabuti,Conditional Expectation,Conditional Probability,Discrete: Conditional Probability Mass Function,Continuous: Conditional Probability Density Function,Conditional Expectation,Discrete:,Con 2、tinuous...