Frontiers of Mathematics in China >

2013 , Vol. 8 >Issue 2: 371 - 391

DOI: https://doi.org/10.1007/s11464-013-0275-0

RESEARCH ARTICLE

Limit theorems of continuous-time random walks with tails

  • Yuqiang LI
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  • School of Finance and Statistics, East China Normal University, Shanghai 200241, China

Received date: 08 Jan 2011

Accepted date: 24 Dec 2012

Published date: 01 Apr 2013

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

We study the functional limits of continuous-time random walks (CTRWs) with tails under certain conditions. We find that the scaled CTRWs with tails converge weakly to an α-stable Lévy process in D([0, 1]) with M1-topology but the corresponding scaled CTRWs converge weakly to the same limit in D([0, 1]) with J1-topology.

Key words： Weak convergence; J1-topology; M1-topology; stable Lévy process

Cite this article

Yuqiang LI . Limit theorems of continuous-time random walks with tails[J]. Frontiers of Mathematics in China, 2013 , 8(2) : 371 -391 . DOI: 10.1007/s11464-013-0275-0

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