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I'm searching a solution for this problem:

Given a segment of length $L$, from $0$ to $L$ divided in $N$ subsegments of the same length, a particle, starting from the subsegment in $x_k$ has a probability to jump to the subsegment in $x_{k+1}$ given by:

$P(x_k\rightarrow x_{k+1})=\frac{1}{2}e^{-\alpha x_k^2}$

and a probability to jump from $x_k$ to $x_{k-1}$ given by: $P(x_k\rightarrow x_{k-1})=1-\frac{1}{2}e^{-\alpha x_k^2}$

What is the probability $P_L(\alpha,L,T)$ to find the particle out from the segment after a time $T$ if the time interval between two jumps is one second?

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    @Didier: 1)yes at least once before time T. 2)Yes, any starting point. 3)I didn't try it.2012-02-15

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