 My Math Forum A serious Random walk needs rigorous proof! PLEASE HELP!
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 May 13th, 2013, 04:24 AM #1 Newbie   Joined: May 2013 Posts: 3 Thanks: 0 A serious Random walk needs rigorous proof! PLEASE HELP! The random walk is the stochastic process Sn := sum_{i=1}^{n} e_i with real-valued, independent, and identically distributed e_i. We say that the random walk is symmetric if the law of e_k is same as that of -e_k. For a symmetric random walk, show the following (1) P(Sn - Sk >= 0) >= 1/2 for k = 1; ... ; n. (2) Fix x > 0. Let  t= inf k >=1 : Sk > x and show that P(Sn > x) >= sum_{i=1}^{n} P(t=k, Sn-Sk>=0) >= 1/2 * sum_{i=1}^{n} P(t=k) (3) Deduce that for any x > 0 and any n P(max_{k=1}^n Sk>x) <=2* P(Sn>x) Tags proof, random, rigorous, serious, walk Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post JoeWright Advanced Statistics 0 February 16th, 2014 04:43 PM rooney_hunter Real Analysis 0 May 13th, 2013 10:29 AM rooney_hunter Economics 0 May 13th, 2013 09:57 AM SimplexLogic Algebra 3 January 26th, 2011 11:40 AM terry Advanced Statistics 3 September 16th, 2008 04:29 PM

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