Journal of Statistical Physics

, Volume 119, Issue 1–2, pp 165–196

Lévy, Ornstein–Uhlenbeck, and Subordination: Spectral vs. Jump Description

Article

DOI: 10.1007/s10955-004-2710-9

Cite this article as:
Eliazar, I. & Klafter, J. J Stat Phys (2005) 119: 165. doi:10.1007/s10955-004-2710-9

Abstract

Unlike Brownian motion, which propagates diffusively and whose sample-path trajectories are continuous, non-Brownian Lévy motions propagate via jumps (flights) and their sample-path trajectories are purely discontinuous. When analyzing systems involving non-Brownian Lévy motions, the common practice is to use either spectral or fractional-calculus methods. In this manuscript we suggest an alternative analytical approach: using the Poisson-superposition jump structure of non-Brownian Lévy motions. We demonstrate this approach in two exemplary topics: (i) systems governed by L évy-driven Ornstein–Uhlenbeck dynamics; and, (ii) systems subject to temporal Lévy subordination. We show that this approach yields answers and insights that are not attainable using spectral methods alone.

Keywords

Non-Brownian Lévy motions selfsimilar Lévy motions Poisson superposition Lévy-driven Ornstein–Uhlenbeck dynamics temporal Lévy subordination 

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of MathematicsBar-Ilan UniversityRamat-GanIsrael
  2. 2.School of Chemistry, Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael

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