Let P(r,t) define the occupation probability, the probability that a particle emulating a random walk will find itself at position r at time t if starts from the origin at time zero.(adsbygoogle = window.adsbygoogle || []).push({});

Let F(r,t) define the first passage probability, the probability that a particle emulating a random walk will find itself at position r at time t FOR THE FIRST TIME if starts from the origin at time zero.

I was reading a book which says this :

"For a random walk to be at position r at time t, the walk must first reach r at some earlier time step t' and then return to r after t-t' additional steps. This connection between F(r,t) and P(r,t) can thus be expressed by the equation

[tex] P(r,t) = \delta_{r0} \delta_{t0} + \sum_{t'\leqt}F(r,t')P(0,t-t') [/tex]

"

Can someone please explain how this is possible?

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# Relation between occupation probability and first passage probability

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