Triangular array limits for continuous time random walks
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.
Year of publication: |
2008
|
---|---|
Authors: | Meerschaert, Mark M. ; Scheffler, Hans-Peter |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 118.2008, 9, p. 1606-1633
|
Publisher: |
Elsevier |
Keywords: | Continuous time random walk Subordinator Hitting time Fractional Cauchy problem |
Saved in:
Online Resource
Saved in favorites
Similar items by person
-
Portfolio modeling with heavy tailed random vectors
Meerschaert, Mark M., (2003)
-
Moment Estimator for Random Vectors with Heavy Tails
Meerschaert, Mark M., (1999)
-
Limit theorems for continuous time random walks with slowly varying waiting times
Meerschaert, Mark M., (2005)
- More ...