EE 126 : Problem Set # 10 Instructor : Jean Walrand
نویسنده
چکیده
Problem 1. Consider a modified random walk defined as follows. If Yn = k, then Yn+1 = max{0,min{k +Xn+1, N}} where the {Xn, n ≥ 1} are i.i.d. with P (Xn = +1) = p = 1−P (Xn = −1). The random variable Y0 is independent of {Xn, n ≥ 1}. Assume that 0 < p < 1. a. Calculate the stationary distribution of {Yn, n ≥ 0}. b. Use a probabilistic (coupling) argument to show that {Yn, n ≥ 0} is asymptotically stationary. c. Write the first step equations for the average time until Yn = 0 given Y0 = k. ——————a. We write and solve the balance equations:
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