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>CLT and<strong>Random</strong><strong>Walk</strong>JeffreySchenkerA GameWorking onthe ProblemInterlude:Gambler’sRuinCLTRand. <strong>Walk</strong><strong>Brownian</strong><strong>Motion</strong>It turns out that this would still hold true if the gamewere much more complicated, with many possibleout comes. As long as it is fair.We findProb(W n ≥ 10) = Prob( 1 √n W n ≥ 10 √ n)→ 1 2 .But we still haven’t figured out if the game ends ornot. For that we need to considerProb(max W n ≥ 10) =?n
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