Stochastic Processes by Wolfgang Paul & Jörg Baschnagel

Author:Wolfgang Paul & Jörg Baschnagel
Language: eng
Format: epub
Publisher: Springer International Publishing, Heidelberg

(4.75)

The function ψ(s) satisfies an inhomogeneous difference equation which we find by considering its behavior upon rescaling the argument, i.e.,

or

(4.76)

The solution of (4.76) consists, again, of two parts: the general solution of the homogeneous equation and a particular solution of the inhomogeneous equation:

As in the case of the Weierstrass random walk, one can show that the singular behavior responsible for 〈τ〉=∞ arises from the homogeneous part,

(4.77)

Equation (4.77) is solved by the ansatz

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.