Let {R_n} be a simple random walk with R_0 = 0, and let T be the smallest index such that k * sqrt(T) < |R_T| for some positive k. What is an expression for the probability distribution of T? Does it have infinite expectation?
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How long for a simple random walk to exceed sqrt(T)?Let {R_n} be a simple random walk with R_0 = 0, and let T be the smallest index such that k * sqrt(T) < |R_T| for some positive k. What is an expression the probability distribution of T? Does it have infinite expectation?
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