How can I find the expected value of a stopping time for a stochastic optimization algorithm?

17 December 2014 0 8K Report

This problem was posed to me by Russ Rinehart. He is interested in finding the expected number of iterations that it takes for a stochastic optimization algorithm, called leapfrogging, to stop. A simplified version of the problem can be formally described as follows.

Let Y(0) = 1 and let U(1), U(2), ... be independent and identically distributed Uniform(0, a) random variables and let Y(t) = Y(t-1)U(t) for t = 1, 2, ....

Let stopping time S be the first time that Y(t)

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