One-dimensional space-discrete transport subject to Levy perturbations

Details One-dimensional space-discrete transport subject to Levy perturbations One-dimensional space-discrete transport subject to Levy perturbations

2008-04-14

arxiv.org/abs/0804.2276v1

Physics

Mathematical Physics

Scientific paper

10.1007/s10955-008-9607-y

In this paper we study a one-dimensional space-discrete transport equation subject to additive Levy forcing. The explicit form of the solutions allows their analytic study. In particular we discuss the invariance of the covariance structure of the stationary distribution for Levy perturbations with finite second moment. The situation of more general Levy perturbations lacking the second moment is considered as well. We moreover show that some of the properties of the solutions are pertinent to a discrete system and are not reproduced by its continuous analogue.

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