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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<strong>Central</strong> <strong>Limit</strong>CLT 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) = (cosh s) n =() n1 + 1 2 s2 + O(s 4 )( ) () nΦ 1 n √n s = 1 + 1 s 22 n + O(s4 /n 2 )Calculus: lim n→∞(1 +xn) n= e x .( )lim n→∞ Φ 1 n √n s = e 1 2 s2 .
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