Limit theorems of continuous-time random walks with tails

Yuqiang Li

doi:10.1007/s11464-013-0275-0

Limit theorems of continuous-time random walks with tails

Yuqiang Li

School of Statistics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	371-391
Number of pages	21
Journal	Frontiers of Mathematics in China
Volume	8
Issue number	2
DOIs	https://doi.org/10.1007/s11464-013-0275-0
State	Published - Apr 2013

Keywords

Weak convergence
stable Lévy process

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10.1007/s11464-013-0275-0

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title = "Limit theorems of continuous-time random walks with tails",

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 L{\'e}vy 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.",

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AB - 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.

KW - Weak convergence

KW - stable Lévy process

UR - https://www.scopus.com/pages/publications/84875524466

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M3 - 文章

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JO - Frontiers of Mathematics in China

JF - Frontiers of Mathematics in China

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Limit theorems of continuous-time random walks with tails

Abstract

Keywords

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