MHB Modified Random Walk: Expected Duration and Recurrence Equation Analysis

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The discussion focuses on deriving a recurrence equation for the expected duration of a modified random walk by conditioning on the first step. It presents a specific equation format involving expected values and parameters represented as ˜p, ˜q, and ˜c. Participants are asked to identify these parameters in relation to the original variables p, q, and r. Additionally, there is a request for clarification on the definition of the modified random walk. The conversation emphasizes the mathematical formulation and relationships necessary for analysis.
Poirot1
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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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