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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

Mathematical Citation Quotient (MCQ) 2018: 0.71

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1435-5337
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Volume 29, Issue 3

# 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:
Published Online: 2016-07-29 | DOI: https://doi.org/10.1515/forum-2016-0031

## Abstract

In this article subordination of random walks in ${ℝ}^{d}$ 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 $2\alpha$-stable process if and only if the Laplace exponent of the corresponding subordinator varies regularly at zero with index $\alpha \in \left(0,1\right]$.

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

## References

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Bertoin J., Lévy Processes, Cambridge University Press, Cambridge, 1996. Google Scholar

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Bingham N. H., Goldie C. M. and Teugels J. L., Regular Variation, Cambridge University Press, Cambridge, 1987. Google Scholar

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Bendikov A. and Saloff-Coste L., Random walks on groups and discrete subordination, Math. Nachr. 285 (2012), 580–605. Google Scholar

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Feller W., An Introduction to Probability Theory and Its Applications, John Wiley & Sons, New York, 1971. Google Scholar

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Jacod J. and Shiryaev A. N., Limit Theorems for Stochastic Processes, Springer, Berlin, 2003. Google Scholar

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Kalenberg O., Foundations of Modern Probability, Springer, Berlin, 2002. Google Scholar

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Sato K.-I., Lévy Processes and Infinitely Divisible Distributions, Cambridge University Press, Cambridge, 1999. Google Scholar

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Schilling R. L., Song R. and Vondraček Z., Bernstein Functions: Theory and Applications, Walter de Gruyter, Berlin, 2012. Google Scholar

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,

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