Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5130077 | Stochastic Processes and their Applications | 2017 | 34 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Mikko S. Pakkanen, Tommi Sottinen, Adil Yazigi,