Discrete Stochastic Processes, Chapter 7: Random Walks ...
7.1 Introduction Definition 7.1.1. Let {X i; i ≥ 1} be a sequence of IID random variables, and let S n = X 1 + X 2 + ··· + X n. The integer-time stochastic process {S n; n ≥ 1} is called a random walk, or, more precisely, the one-dimensional random walk based on {X i; i ≥ 1}. For any given n, S n is simply a sum of IID random ...
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