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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WienerCLT and<strong>Random</strong><strong>Walk</strong>JeffreySchenkerA GameWorking onthe ProblemInterlude:Gambler’sRuinCLTRand. <strong>Walk</strong><strong>Brownian</strong><strong>Motion</strong>Norbert Wiener realized in 1932that this headed somewhere asn → ∞He showed there is a probabilitydistribution on the space offunctions of t such that therandom function W satisfiesIt is continuous (no jumps!)W (0) = 0W (t) is √ t× a standard normalrandom variable for each t.
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