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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

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1435-5337
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Volume 29, Issue 3

Issues

On subordinate random walks

Ante Mimica
  • Corresponding author
  • Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2016-07-29 | DOI: https://doi.org/10.1515/forum-2016-0031

Abstract

In this article subordination of random walks in d is considered. We prove that subordination of random walks in the sense of [4] yields the same process as subordination in the sense of Lévy processes. Furthermore, we prove that appropriately scaled subordinate random walk converges to a multiple of a rotationally 2α-stable process if and only if the Laplace exponent of the corresponding subordinator varies regularly at zero with index α(0,1].

Keywords: Random walk; subordination; compound Poisson process; Lévy process; regular variation,invariance principle

MSC 2010: 60J75; 60G51; 60G52; 60F17

References

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About the article


Received: 2016-02-06

Revised: 2016-06-03

Published Online: 2016-07-29

Published in Print: 2017-05-01


Funding Source: Hrvatska Zaklada za Znanost

Award identifier / Grant number: 3526

Research supported by Croatian Science Foundation under the project 3526.


Citation Information: Forum Mathematicum, Volume 29, Issue 3, Pages 653–664, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2016-0031.

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Alexander Bendikov, Wojciech Cygan, and Bartosz Trojan
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