2012/09/07 by Andreas Basse-O’Connor, Andreas Basse-O'Connor, J. Rosiński +3 · 2 citations
Economics, Econometrics and Finance · Mathematics · #Banking stability, regulation, efficiency #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #math.PR
paper · pdf · doi:10.48550/arxiv.1209.1644
See arXiv:1404.7598 for a major revision under a new title, improved and refocussed exposition
openalex publication_date 2012/09/07 · arxiv created 2014/05/01 · arxiv updated 2014/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper gives a complete characterization of infinitely divisible semimartingales, i.e., semimartingales whose finite dimensional distributions are infinitely divisible. An explicit and essentially unique decomposition of such semimartingales is obtained. A new approach, combining series decompositions of infinitely divisible processes with detailed analysis of their jumps, is presented. As an ilustration of the main result, the semimartingale property is explicitely determined for a large class of stationary increment processes and several examples of processes of interest are considered. These results extend Stricker's theorem characterizing Gaussian semimartingales and Knight's theorem describing Gaussian moving average semimartingales, in particular.