Dynamics of confined Levy flights in terms of (Levy) semigroups

Details Dynamics of confined Levy flights in terms of (Levy) semigroups Dynamics of confined Levy flights in terms of (Levy) semigroups

2011-06-08

arxiv.org/abs/1106.1530v3

Physics

Condensed Matter

Statistical Mechanics

New title, abstract, figures, a number of text amendments

Scientific paper

The master equation for a probability density function (pdf) driven by L\'{e}vy noise, if conditioned to conform with the principle of detailed balance, admits a transformation to a contractive strongly continuous semigroup dynamics. Given a priori a functional form of the semigroup potential, we address the ground-state reconstruction problem for generic L\'{e}vy-stable semigroups, for {\em all} values of the stability index $\mu \in (0,2)$. That is known to resolve an invariant pdf for confined L\'{e}vy flights (e.g. the former jump-type process). Jeopardies of the procedure are discussed, with a focus on: (i) when an invariant pdf actually is an asymptotic one, (ii) subtleties of the pdf $\mu $-dependence in the vicinity and sharply {\em at} the boundaries 0 and 2 of the stability interval, where jump-type scenarios cease to be valid.

Affiliated with

Also associated with

No associations

Rating

Dynamics of confined Levy flights in terms of (Levy) semigroups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dynamics of confined Levy flights in terms of (Levy) semigroups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dynamics of confined Levy flights in terms of (Levy) semigroups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-320083