Peter Imkeller and Ilya Pavlyukevich 2006 J. Phys. A: Math. Gen. 39 L237 doi:10.1088/0305-4470/39/15/L01
Lévy flights: transitions and meta-stability
FREE ARTICLEPeter Imkeller and Ilya Pavlyukevich
Show affiliationsLETTER TO THE EDITOR
We consider Lévy flights of stability index α 
(0, 2) in a potential landscape in the limit of a small noise parameter. We give a purely probabilistic description of the random dynamics on the basis of a special decomposition of the driving Lévy processes into independent small jumps and compound Poisson parts. We prove that escape times from a potential well are exponentially distributed and their mean values increase as a power ε−α of the noise intensity ε. This allows us to obtain meta-stability results for a jump diffusion in a double-well potential.
- PACS
- MSC
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82C41 Dynamics of random walks, random surfaces, lattice animals, etc. (See also 60G50)
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) (See also 60H10)
- Subjects
- Dates
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Issue 15 (14 April 2006)
Received 9 January 2006, in final form 10 March 2006
Published 29 March 2006
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Lévy flights: transitions and meta-stability
Peter Imkeller and Ilya Pavlyukevich 2006 J. Phys. A: Math. Gen. 39 L237
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