Sn denotes the position is at during the nth time of the random walk. For example, if you're on the 3rd position at the 10th time, S10 = 3.
Sn denotes the position is at during the nth time of the random walk. For example,...
For the random walk of Example 4.18, use the strong law of large numbers to give another proof that the Markov chain is transient when p [Hint: Note that the state at time n can be written as Σίι Yi, where the Y's are independent and PO-1)-p-1-PY,--1). Argue that if p 〉 흘, then, by the strong law of large numbers. Ση-1 Ý, oo as n oo and hence the initial state 0 can be visited only finitely often, and...