English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Consider a multivariate L\'evy-driven Ornstein-Uhlenbeck process where thestationary distribution or background driving L\'evy process is from aparametric family. We derive the likelihood function assuming that theinnovation term is absolutely continuous. Two examples are studied in detail:the process where the stationary distribution or background driving L\'evyprocess is given by a weak variance alpha-gamma process, which is amultivariate generalisation of the variance gamma process created using weaksubordination. In the former case, we give an explicit representation of thebackground driving L\'evy process, leading to an innovation term which isdiscrete and continuous mixture, allowing for the exact simulation of theprocess, and a separate likelihood function. In the latter case, we show theinnovation term is absolutely continuous. The results of a simulation studydemonstrate that maximum likelihood numerically computed using Fourierinversion can be applied to accurately estimate the parameters in both cases.

Calibration for multivariate L\'evy-driven Ornstein-Uhlenbeck processes with applications to weak subordination