کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1156938 958900 2008 28 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Triangular array limits for continuous time random walks
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Triangular array limits for continuous time random walks
چکیده انگلیسی

A continuous time random walk (CTRW) is a random walk subordinated to a renewal process, used in physics to model anomalous diffusion. Transition densities of CTRW scaling limits solve fractional diffusion equations. This paper develops more general limit theorems, based on triangular arrays, for sequences of CTRW processes. The array elements consist of random vectors that incorporate both the random walk jump variable and the waiting time preceding that jump. The CTRW limit process consists of a vector-valued Lévy process whose time parameter is replaced by the hitting time process of a real-valued nondecreasing Lévy process (subordinator). We provide a formula for the distribution of the CTRW limit process and show that their densities solve abstract space–time diffusion equations. Applications to finance are discussed, and a density formula for the hitting time of any strictly increasing subordinator is developed.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 118, Issue 9, September 2008, Pages 1606–1633
نویسندگان
, ,