A markov chain whose state space is given by the integers i, Ask an Expert

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A Markov chain whose state space is given by the integers i = 0, ±1, ±2, ... is said to be a random walk if, for some number 0 <>p 1, Pi,i+1 = p = 1 - Pi,i-1, i = 0, ±1, ...

The preceding Markov chain is called a random walk for we may think of it as being a model for an individual walking on a straight line who at each point of time either takes one step to the right with probability p or one step to the left with probability 1 - p.

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