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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:127

Article

Pakkanen, Mikko S.^1,2  Sottinen, Tommi³  Yazigi, Adil³ 

[1] Imperial Coll London, Dept Math, South Kensington Campus, London SW7 2AZ, England

[2] Aarhus Univ, CREATES, Aarhus, Denmark

[3] Univ Vaasa, Dept Math & Stat, POB 700, FIN-65101 Vaasa, Finland

关键词: 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;   

DOI  :  10.1016/j.spa.2016.06.025

来源: Elsevier

【 摘 要 】

We study whether a multivariate Levy-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 Levy-driven moving average processes under natural non-degeneracy conditions on the kernel function of the process and on the driving Levy process. We discuss in depth how to verify these conditions in practice. As concrete examples, to which our results apply, we consider fractional Levy processes and multivariate Levy-driven Ornstein-Uhlenbeck processes. (C)2016 Elsevier B.V. All rights reserved.

【 授权许可】

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