Integrability conditions for space-time stochastic integrals: Theory and applications

Carsten Chong; Claudia Kluppelberg

doi:10.3150/14-BEJ640

Integrability conditions for space-time stochastic integrals: Theory and applications

Carsten Chong, Claudia Kluppelberg

Chair of Mathematical Statistics

Technical University of Munich

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

14 Scopus citations

Abstract

We derive explicit integrability conditions for stochastic integrals taken over time and space driven by a random measure. Our main tool is a canonical decomposition of a random measure which extends the results from the purely temporal case.We show that the characteristics of this decomposition can be chosen as predictable strict random measures, and we compute the characteristics of the stochastic integral process. We apply our conditions to a variety of examples, in particular to ambit processes, which represent a rich model class.

Original language	English
Pages (from-to)	2190-2216
Number of pages	27
Journal	Bernoulli
Volume	21
Issue number	4
DOIs	https://doi.org/10.3150/14-BEJ640
State	Published - 1 Nov 2015

Keywords

Ambit process
Continuous-time moving average
Integrability conditions
Lévy basis
Martingale measure
Predictable characteristics
Random measure
Stochastic integration
Stochastic partial differential equation
SupCARMA
SupCOGARCH
SupOU
Volterra process

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abstract = "We derive explicit integrability conditions for stochastic integrals taken over time and space driven by a random measure. Our main tool is a canonical decomposition of a random measure which extends the results from the purely temporal case.We show that the characteristics of this decomposition can be chosen as predictable strict random measures, and we compute the characteristics of the stochastic integral process. We apply our conditions to a variety of examples, in particular to ambit processes, which represent a rich model class.",

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AB - We derive explicit integrability conditions for stochastic integrals taken over time and space driven by a random measure. Our main tool is a canonical decomposition of a random measure which extends the results from the purely temporal case.We show that the characteristics of this decomposition can be chosen as predictable strict random measures, and we compute the characteristics of the stochastic integral process. We apply our conditions to a variety of examples, in particular to ambit processes, which represent a rich model class.

KW - Ambit process

KW - Continuous-time moving average

KW - Integrability conditions

KW - Lévy basis

KW - Martingale measure

KW - Predictable characteristics

KW - Random measure

KW - Stochastic integration

KW - Stochastic partial differential equation

KW - SupCARMA

KW - SupCOGARCH

KW - SupOU

KW - Volterra process

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JO - Bernoulli

JF - Bernoulli

IS - 4

ER -

Integrability conditions for space-time stochastic integrals: Theory and applications

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Keywords

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