Abstract
Which Lévy processes satisfy Hunt’s hypothesis (H) is a long-standing open problem in probabilistic potential theory. The study of this problem for one-dimensional Lévy processes suggests us to consider (H) from the point of view of the sum of Lévy processes. In this paper, we present theorems and examples on the validity of (H) for the sum of two independent Lévy processes. We also give a novel condition on the Lévy measure which implies (H) for a large class of one-dimensional Lévy processes.
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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant No. 11771309), Natural Science and Engineering Research Council of Canada (Grant No. 311945-2013) and the Fundamental Research Funds for the Central Universities of China. The authors wish to thank the referee for the helpful comments which led to an improved version of the paper.
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Hu, ZC., Sun, W. Hunt’s Hypothesis (H) for the Sum of Two Independent Lévy Processes. Commun. Math. Stat. 6, 227–247 (2018). https://doi.org/10.1007/s40304-018-0136-y
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DOI: https://doi.org/10.1007/s40304-018-0136-y