Lévy, ornstein-uhlenbeck, and subordination: Spectral vs. Jump description

Iddo Eliazar, Joseph Klafter

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)165-196
Number of pages32
JournalJournal of Statistical Physics
Volume119
Issue number1-2
DOIs
StatePublished - Apr 2005

Keywords

  • Lévy-driven Ornstein-Uhlenbeck dynamics
  • Non-Brownian Lévy motions
  • Poisson superposition
  • Selfsimilar Lévy motions
  • Temporal Lévy subordination

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