MFPT at x=0: —
Mean first passage time: T(x) is the average time for a random walker starting at x to first reach the absorbing boundary at x*.
It satisfies the BVP: −D·T''(x) + v·T'(x) = −1 with T(x*)=0, T'(0)=0 (reflecting left boundary).
Exact solution: T(x) = (1/v)[x − x*] + (D/v²)[e^(v·x/D) − e^(v·x*/D)] / [v/D · e^(v·x*/D)] for v≠0.
Large drift v>0 (pushed toward target) → small MFPT; v<0 (pushed away) → large MFPT; D large → flat MFPT.
Exact solution: T(x) = (1/v)[x − x*] + (D/v²)[e^(v·x/D) − e^(v·x*/D)] / [v/D · e^(v·x*/D)] for v≠0.
Large drift v>0 (pushed toward target) → small MFPT; v<0 (pushed away) → large MFPT; D large → flat MFPT.