MSU Find the Integral Representation of The Transition Probabilities Questions

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sqsqpunb

Mathematics

Michigan State University

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In #3, part 2, the formula for E(X) is wrong. The factors p_2 and q_2 should be multiplied by 2, i.e.

E(X) = (2 p_2+p_1-q_1-2 q_2)t +y

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3. (20 pts) Let Xų denote the position of a random walker on the integer lattice Z at time t (continuous time). The nonzero transition rates in the Q-matrix are Q2-2,0 = P2, Q.2–1,1 = P1, Qz+1,2 = 21, Q1+2,1 = 42 where 0 < Pi
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Explanation & Answer

Attached.

3. Given that
𝑄𝑥−2,𝑥 = 𝑝2 , 𝑄𝑥−1,𝑥 = 𝑝1 ,
𝑄𝑥+1,𝑥 = 𝑞1 ,
𝑄𝑥+2,𝑥 = 𝑞2 ,
Initial conditions,
𝑃𝑥−2 (𝑥; 0) = 0, 𝑃𝑥−1 (𝑥; 0) = ...


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