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thanks for your effort. Yes finally E is based on four values. So if i change v i'll get a different E value for the same u. What i need is an another simpler equation for E, not with all these matrices. I know it from simulations that E=2(n-v) if v > u and E=2(n-u) if v < u. But is it possible to get these results from the equation given in the question? I saw a paper with similar problem. They've solved it using recurrence relations.
Title: "the random walk between a reflecting and an absorbing barrier". (I couldn't use the url)
Yes thats right.
If xp > u then E(xp) linearly decreases as xp increases.
sorry about that... i was confused while typing. I've changed it now.
I've modified my question. Hope its clear now.
let say u=2 and xp=1;
then
Q will be like this,
G(1) depends on 'u'; It has 0.5 in u-1 and u+1 th position. (count starts from 0);
P(xp) depends on xp ; It has 0.5 in xp-1 and xp+1 th position.
hi, i have this equation
If u=2 and xp=1;
then,
(G(1) - (n*1) matrix ,depends on 'u'; It has 0.5 in u-1 and u+1 th position. (count starts from 0); P(xp) - (1*n) matrix ,depends on xp ; It has 0.5 in xp-1 and xp+1 th position.)
If xp < u then the E(xp) is constant, if xp > u then E(xp) is linearly decreasing. But is it possible to get a final simple equation with notations u , xp and n(matrix size)?
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