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> <strong>Theorem</strong> V2.0CLT and<strong>Random</strong><strong>Walk</strong>JeffreySchenkerA GameWorking onthe ProblemInterlude:Gambler’sRuinCLTRand. <strong>Walk</strong><strong>Brownian</strong><strong>Motion</strong>For each n let W n (t) be a function with( ) iW n = √ 1 Wni , nthen as a random function W n converges to Wiener’srandom function W . (Convergence in distribution.)In particular,Prob(max |W i| > $10) → Prob( max |W (t)| > 0) = 1,1≤i≤n 0≤t≤1so our game certainly ends.
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