Limit theorems and governing equations for Levy walks

Magdziarz M, Scheffler HP, Straka P, & Żebrowski P (2015). Limit theorems and governing equations for Levy walks. Stochastic Processes and their Applications 125 (11): 4021-4038. DOI:10.1016/j.spa.2015.05.014.

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Abstract

The Levy Walk is the process with continuous sample paths which arises from consecutive linear motions of i.i.d. lengths with i.i.d. directions. Assuming speed 1 and motions in the domain of beta-stable attraction, we prove functional limit theorems and derive governing pseudo-differential equations for the law of the walker's position. Both Levy Walk and its limit process are continuous and ballistic in the case beta epsilon(0,1). In the case beta epsilon (1,2), the scaling limit of the process is beta-stable and hence discontinuous. This result is surprising, because the scaling exponent 1/beta on the process level is seemingly unrelated to the scaling exponent 3-beta of the second moment. For beta=2, the scaling limit is Brownian motion.

Item Type: Article
Uncontrolled Keywords: Levy walk; domain of attraction; governing equation
Research Programs: Advanced Systems Analysis (ASA)
Bibliographic Reference: Stochastic Processes and their Applications; 125(11):4021-4038 (November 2015) (Published online 5 June 2015)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 08:53
Last Modified: 14 Sep 2016 12:25
URI: http://pure.iiasa.ac.at/11397

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