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

Mikko S. Pakkanen, Tommi Sottinen () and Adil Yazigi

Stochastic Processes and their Applications, 2017, vol. 127, issue 3, 749-782

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.

Keywords: Small ball probability; Conditional full support; Moving average process; Multivariate Lévy process; Convolution determinant; Fractional Lévy process; Lévy-driven OU process; Lévy copula; Lévy mixing; Multivariate subordination (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2016.06.025

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