On the conditional small ball property of multivariate Lévy-driven moving average processes
File(s)
Accepted version
Author(s)
Pakkanen, MS
Sottinen, T
Yazigi, A
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.
Date Issued
2016-07-05
Date Acceptance
2016-06-27
Citation
Stochastic Processes and their Applications, 2016, 127 (3), pp.749-782
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
Academy of Finland
Grant Number
258042
Subjects
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
60G10, 60G17 (Primary) 60G22, 60G51 (Secondary)
0104 Statistics
1502 Banking, Finance And Investment
Publication Status
Published