The probability density function of a random walk with constant diffusion D in 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The probability density function of a random walk with constant diffusion D
in 0 <x <L is
P(r,t) = Ne-at sin(kæ'),
where N and a are constants, k = T/(2L), and L is the length of the domain.
(a) What types of boundary conditions are satisfied at r = 0 and r = L?
(b) Find the survival probability S(t) of this random walk, and find an
expression for the constant N in terms of L.
(c) Find the mean exit time in terms of a.
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