Central Limit Theorem, Random Walk, Brownian Motion
Central Limit Theorem, Random Walk, Brownian Motion
Central Limit Theorem, Random Walk, Brownian Motion
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Moment generating functionCLT and<strong>Random</strong><strong>Walk</strong>JeffreySchenkerA GameWorking onthe ProblemInterlude:Gambler’sRuinCLTRand. <strong>Walk</strong><strong>Brownian</strong><strong>Motion</strong>Φ n (s) = AvW n = ∑ n i=1 w i as before.Φ n (0) = 1Φ n (s) ∼ 2 −n e sn as s → +∞Φ n (s) ∼ 2 −n e −sn as s → −∞( )e sW nΦ n actually contains all the information on theprobability distribution of W n !
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