Modified Random Walk: Expected Duration and Recurrence Equation Analysis

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The discussion focuses on the expected duration of a modified random walk, establishing a recurrence equation of the form E[a] = ˜pE[a+1] + ˜qE[a-1] + ˜c. The values of ˜p, ˜q, and ˜c are to be clearly defined in terms of the parameters p, q, and r. Participants emphasize the importance of conditioning on the first step to derive this equation, which is crucial for understanding the behavior of the modified random walk.

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(1)Consider the expected duration of the modified random walk. Show that conditioning on the first step produces a recurrence equation of the following form.​
Ea = ˜pEa+1 + ˜qEa−1 + ˜c.
(2)Clearly identify the values of ˜p, ˜q and ˜c in terms of p, q and r.
Thanks
 
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Poirot said:

(1)Consider the expected duration of the modified random walk. Show that conditioning on the first step produces a recurrence equation of the following form.​
Ea = ˜pEa+1 + ˜qEa−1 + ˜c.
(2)Clearly identify the values of ˜p, ˜q and ˜c in terms of p, q and r.
Thanks


Please post the entire question, in particular the definition of your modified random walk

CB
 

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