random_walk - Summer 2007 STAT333 Summary of the Random...

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Summer 2007 STAT333 Summary of the Random walk Random walk is a simple stochastic process, which can be regarded as an example for the renewal process, and can also be regarded as an example for the discrete Markov process. The following are some formulas you need to memorize. You should understand them before memorizing them. DeFnition of random walk process (a) We assume that the walk starts at the origin 0 (that is, X 0 = 0). (b) On each step the process either jumps one unit to the right or one unit to the left. Therefore, we have X n +1 = X n + I n +1 , where I n = b 1 if the process jumps to the right by one unit at step n + 1 1 if the process jumps to the left by one unit at step n + 1 . The jumps themselves (+ or -) can be viewed as a sequence of Bernoulli trials (or coin tosses) where p is the probability of a jump to the right (+) and q = 1 p is the probability of a jump to the left (-). (c) Let
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random_walk - Summer 2007 STAT333 Summary of the Random...

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