Relation between occupation probability and first passage probability

mathman

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All the expression is saying is that a particle arriving at r at time t will have had a first arrival at r at time t' (which may = t) ahd then arrive at a relative position of 0 in time t-t'. The delta function term simply says that P(0,0) reflects the fact that it was at 0 to start with.
 
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All the expression is saying is that a particle arriving at r at time t will have had a first arrival at r at time t' (which may = t) ahd then arrive at a relative position of 0 in time t-t'. The delta function term simply says that P(0,0) reflects the fact that it was at 0 to start with.
He is describing relative position zero using the same probability distribution P? So he is making the assumption there that P doesn't change once the thing reaches r? He hasn't mentioned this explicitly.
 

mathman

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There is an implicit assumption of stationarity, i.e. the distribution depends only on time difference, not absolute time.
 
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Okay! Thanks.
 

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