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On the conditional small ball property of multivariate Lévy-driven moving average processes

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Title: On the conditional small ball property of multivariate Lévy-driven moving average processes
Authors: Pakkanen, MS
Sottinen, T
Yazigi, A
Item Type: Journal Article
Abstract: We study whether a multivariate Lévy-driven moving average process can shadow arbitrarily closely any continuous path, starting from the present value of the process, with positive conditional probability, which we call the conditional small ball property. Our main results establish the conditional small ball property for Lévy-driven moving average processes under natural non-degeneracy conditions on the kernel function of the process and on the driving Lévy process. We discuss in depth how to verify these conditions in practice. As concrete examples, to which our results apply, we consider fractional Lévy processes and multivariate Lévy-driven Ornstein–Uhlenbeck processes.
Issue Date: 5-Jul-2016
Date of Acceptance: 27-Jun-2016
URI: http://hdl.handle.net/10044/1/37433
DOI: https://dx.doi.org/10.1016/j.spa.2016.06.025
ISSN: 0304-4149
Publisher: Elsevier
Start Page: 749
End Page: 782
Journal / Book Title: Stochastic Processes and their Applications
Volume: 127
Issue: 3
Copyright Statement: © 2016 Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor/Funder: Academy of Finland
Funder's Grant Number: 258042
Keywords: Science & Technology
Physical Sciences
Statistics & Probability
Mathematics
Small ball probability
Conditional full support
Moving average process
Multivariate Levy process
Convolution determinant
Fractional Levy process
Levy-driven OU process
Levy copula
Levy mixing
Multivariate subordination
INFINITELY DIVISIBLE PROCESSES
FULL SUPPORT
TRANSACTION COSTS
SMALL DEVIATIONS
FRACTIONAL LEVY
NO-ARBITRAGE
REPRESENTATIONS
SEMIMARTINGALES
DISTRIBUTIONS
BOUNDEDNESS
math.PR
math.PR
60G10, 60G17 (Primary) 60G22, 60G51 (Secondary)
0104 Statistics
1502 Banking, Finance And Investment
Statistics & Probability
Publication Status: Published
Appears in Collections:Financial Mathematics
Mathematics
Faculty of Natural Sciences



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