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Licensed Unlicensed Requires Authentication Published by De Gruyter July 29, 2016

On subordinate random walks

  • Ante Mimica
From the journal Forum Mathematicum

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].


Communicated by Ichiro Shigekawa


Award Identifier / Grant number: 3526

Funding statement: Research supported by Croatian Science Foundation under the project 3526.

References

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Received: 2016-2-6
Revised: 2016-6-3
Published Online: 2016-7-29
Published in Print: 2017-5-1

© 2017 by De Gruyter

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