Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10527174 | Stochastic Processes and their Applications | 2015 | 18 Pages |
Abstract
The Lévy 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 β-stable attraction, we prove functional limit theorems and derive governing pseudo-differential equations for the law of the walker's position. Both Lévy Walk and its limit process are continuous and ballistic in the case βâ(0,1). In the case βâ(1,2), the scaling limit of the process is β-stable and hence discontinuous. This result is surprising, because the scaling exponent 1/β on the process level is seemingly unrelated to the scaling exponent 3âβ of the second moment. For β=2, the scaling limit is Brownian motion.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
M. Magdziarz, H.P. Scheffler, P. Straka, P. Zebrowski,