期刊
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
卷 125, 期 11, 页码 4021-4038出版社
ELSEVIER
DOI: 10.1016/j.spa.2015.05.014
关键词
Levy walk; Domain of attraction; Governing equation
资金
- NCN Maestro [2012/06/A/ST1/00258]
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 = 2, the scaling limit is Brownian motion. (C) 2015 Elsevier B.V. All rights reserved.
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