Stochastic comparison and preservation of positive correlations for Lévy-type processes. (English) Zbl 1180.60062
The author presents some sufficient and some necessary conditions for the preservation of positive correlations of Lévy type processes. Because of the jump processes none of these conditions are necessary and sufficient. The preservation of positive correlations is related with the stochastic monotone or more generally with the stochastic comparison. The proof of the theorems is mainly based on the limit theorem and some convergence properties of Lévy type processes. Under additional assumptions some of the necessary conditions for stochastic comparison are proved to be also sufficient.
Reviewer: A. Świerniak (Gliwice)
MSC:
| 60J25 | Continuous-time Markov processes on general state spaces |
| 60J75 | Jump processes (MSC2010) |
| 60F05 | Central limit and other weak theorems |
| 60G44 | Martingales with continuous parameter |
| 60G57 | Random measures |
| 60K15 | Markov renewal processes, semi-Markov processes |
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