کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10527174 | 958721 | 2015 | 18 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Limit theorems and governing equations for Lévy walks
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 125, Issue 11, November 2015, Pages 4021-4038
Journal: Stochastic Processes and their Applications - Volume 125, Issue 11, November 2015, Pages 4021-4038
نویسندگان
M. Magdziarz, H.P. Scheffler, P. Straka, P. Zebrowski,