Relation between occupation probability and first passage probability

mathman

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.

WiFO215

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

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

Okay! Thanks.

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