2021/05/26 by Jevgeņijs Ivanovs, Ivanovs, Jevgenijs, Jakob D. Thøstesen +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60F17 (Secondary) #60G51 (Primary) 60G17 #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Statistical Distribution Estimation and Applications #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2105.12539
openalex publication_date 2021/05/26 · openalex created_date 2022/11/30 · openalex updated_date 2026/07/28
This paper provides a multivariate extension of Bertoin's pathwise construction of a Lévy process conditioned to stay positive/negative. Thus obtained processes conditioned to stay in half-spaces are closely related to the original process on a compact time interval seen from its directional extremal points. In the case of a correlated Brownian motion the law of the conditioned process is obtained by a linear transformation of a standard Brownian motion and an independent Bessel-3 process. Further motivation is provided by a limit theorem corresponding to zooming in on a Lévy process with a Brownian part at the point of its directional infimum. Applications to zooming in at the point furthest from the origin are envisaged.