Recent content by rta1988

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    Asymmetric Random Walk on the Set of Integers

    u_{i+1} - u_i = P(X_1 = 0|X_0 = -1) - P(X_1 = 0|X_0 = 1)q + P(X_1 = 0|X_0 = -1)p u_{i+1} - u_i = ? u_{i+1} - u_i = (q/p)[P(X_1 = 0|X_0 = 1)q + P(X_1 = 0|X_0 = -1)p - P(X_1 = 0|X_0 = 1)] u_{i+1} - u_i = a(u_i - u_{i-1}) by mathematical induction it's easy to get: a^i(u_1 - u_0). But it's...
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    Asymmetric Random Walk on the Set of Integers

    Thanks. I understand this. I guess the question was just really austerely written. Plus, I'm new to stochastic processes and it's been a while since I've taken probability. I'm wondering if you can walk me through a few more. By conditioning according to the possible values of X_1 (first-step...
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    Asymmetric Random Walk on the Set of Integers

    I was going to try and point out something wrong, but I see you can edit the above message now. This is my first time. Hope to get some good feedback! :)
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    Asymmetric Random Walk on the Set of Integers

    Homework Statement Give the value of u_0.Homework Equations Let p>q>0 with p+q = 1 and a = q/p < 1. Let X_n denote the random walk with transitions X_{n+1} = CASE 1: X_n + 1 with probability p and CASE 2: X_n - 1 with probability q. For i ≥ 0, we set u_i = P(X_n = 0 for some n ≥ 0|X_0 = i)...