Competition between Lévy jumps and continuous drift

I.M. Sokolov and V.V. Belik

Physica A: Statistical Mechanics and its Applications, 2003, vol. 330, issue 1, 46-52

Abstract: Motivated by certain birth–death processes with strongly fluctuating birth rates, we consider a level-crossing problem for a random process being a superposition of a continuous drift to the left and jumps to the right. The lengths of the corresponding jumps follow a one-sided extreme Lévy-law of index α. We concentrate on the case 0<α<1 and discuss the probability of crossing a left boundary (“extinction”). We show that this probability decays exponentially as a function of the initial distance to the boundary. Such behavior is universal for all α<1 and is exemplified by an exact solution for the special case α=12. The splitting probabilities are also discussed.

Keywords: Asymmetric Lévy flights; First passage time; Splitting probability (search for similar items in EconPapers)
Date: 2003
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:330:y:2003:i:1:p:46-52

DOI: 10.1016/j.physa.2003.08.028

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