Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-23T05:03:13.214Z Has data issue: false hasContentIssue false
  • English
  • Français

A Lévy Process whose Jumps are Dragged by a Spherical Dynamical System

Part of: Stochastic processes Limit theorems

Published online by Cambridge University Press:  14 July 2016

Brice Franke
Brice Franke*
Affiliation:
Ruhr-Universität Bochum
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We investigate the large scale behaviour of a Lévy process whose jump magnitude follows a stable law with spherically inhomogenous scaling coefficients. Furthermore, the jumps are dragged in the spherical direction by a dynamical system which has an attractor.

Keywords

Scaled Lévy processdynamical systemlarge deviationcentral limit theorem

MSC classification

Secondary: 60G51: Processes with independent increments; L'evy processes 60F17: Functional limit theorems; invariance principles
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 3 , September 2007 , pp. 732 - 741
Copyright
Copyright © Applied Probability Trust 2007 

References

Ancey, C., Böhm, T., Jodeau, M. and Frey, P. (2006). Statistical description of sediment transport experiments. Physical Reviews E 74, 011302.Google Scholar
Aref, H. (1990). Chaotic advection of fluid particles. Philos. Trans. Physical Sci. Eng. 333, 273–288.Google Scholar
Bagnold, R. (1973). The nature of saltation and bed-load transport in water. Proc. R. Soc. London A 332, 473–504.Google Scholar
Buescu, J. (1997). Exotic Attractors. From Liapunov Stablity to Riddled Basins (Progr. Math. 153). Birkhäuser, Basel.Google Scholar
Franke, B. (2006). The scaling limit behaviour of periodic stable-like processes. Bernoulli 12, 551–570.Google Scholar
Gani, J. (1988). A correlated random walk for the transport and sedimentation of particles. In A Celebration of Applied Probability (J. Appl. Prob. Spec. Vol. 25A) Applied Probability Trust, Sheffield, pp. 335–346.Google Scholar
Gani, J. and Todorovic, P. (1983). A model for the transport of solid particles in a fluid flow. Stoch. Process. Appl. 14, 1–17.Google Scholar
Jacod, J. and Shiryaev, A. (2003). Limit Theorems for Stochastic Processes, 2nd edn. Springer, Berlin.Google Scholar
Hult, H. and Lindskog, F. (2005). Extremal behaviour of regularly varying stochastic processes. Stoch. Process. Appl. 115, 249–274.Google Scholar
Kawakami, A. and Funakoshi, M. (1999). Chaotic motion of fluid particles around a rotating elliptic vortex in a linear shear flow. Fluid Dynamics Res. 25, 167–193.Google Scholar
Kida, S. (1981). Motion of an elliptic vortex in a uniform shear flow. J. Physical Soc. Japan 50, 3517–3520.Google Scholar
Maxey, M. (1990). On the advection of spherical and non-spherical particles in a non-uniform flow. Philos. Trans. Physical Sci. Eng. 333, 289–307.Google Scholar
Pickard, D. and Tory, E. (1977). A Markov model for sedimentation. J. Math. Anal. Appl. 60, 349–369.Google Scholar
Polvani, L. and Wisdom, J. (1990). Chaotic Lagrangian trajectories around an elliptic vortex patch embedded in a constant and uniform background shear flow. Physics Fluids A 2, 123–126.Google Scholar
Sato, K. (1999). Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press.Google Scholar
Wentzell, A. D. (1990). Limit Theorems on Large Deviations for Markov Stochastic Processes. Kluwer, Dordrecht.Google Scholar