Multistable processes and localizability

Kenneth John Falconer; Lining Liu

doi:10.1080/15326349.2012.699766

Multistable processes and localizability

Kenneth John Falconer, Lining Liu

Pure Mathematics

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

Abstract

We use characteristic functions to construct alpha-multistable measures and integrals, where the measures behave locally like stable measures, but with the stability index alpha(x) varying with x. This enables us to construct alpha-multistable processes on R, that is processes whose scaling limit at time t is an alpha(t)-stable process. We present several examples of such multistable processes and examine their localisability.

Original language	English
Pages (from-to)	503-526
Number of pages	23
Journal	Stochastic Models
Volume	28
Issue number	3
Early online date	1 Aug 2012
DOIs	https://doi.org/10.1080/15326349.2012.699766
Publication status	Published - 2012

Keywords

Localizable
Multistable measure
Multistable process
Scaling limit
Stable process

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10.1080/15326349.2012.699766

KF LL SMRevised
This is an Author's Accepted Manuscript of an article published in Stochastic Models, 2012 copyright Taylor & Francis, available online at: http://www.tandfonline.com/10.1080/15326349.2012.699766
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Cite this

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AU - Liu, Lining

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AB - We use characteristic functions to construct alpha-multistable measures and integrals, where the measures behave locally like stable measures, but with the stability index alpha(x) varying with x. This enables us to construct alpha-multistable processes on R, that is processes whose scaling limit at time t is an alpha(t)-stable process. We present several examples of such multistable processes and examine their localisability.

KW - Localizable

KW - Multistable measure

KW - Multistable process

KW - Scaling limit

KW - Stable process

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U2 - 10.1080/15326349.2012.699766

DO - 10.1080/15326349.2012.699766

M3 - Article

SN - 1532-6349

VL - 28

SP - 503

EP - 526

JO - Stochastic Models

JF - Stochastic Models

IS - 3

ER -

Multistable processes and localizability

Abstract

Keywords

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