Abstract
The main goal of this paper is to establish necessary and sufficient conditions for stochastic comparison of two general Lévy-type processes on ℝd. By refining the test functions in Wang (Acta Math. Sin. Engl. Ser. 25:741–758, 2009), mainly the test functions of diffusion coefficients, we get the necessary conditions. The sufficiency of the conditions is obtained by constructing a new sequence of finite Lévy measures {ν n} n≥1 different from the one in Wang (Acta Math. Sin. Engl. Ser. 25:741–758, 2009) to approach the Lévy measure ν.
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Acknowledgements
Research supported in part by NSFC (No. 10971012; No. 11026126). The author thanks the referee for corrections and helpful comments.
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Wang, JM. Stochastic Comparison for Lévy-Type Processes. J Theor Probab 26, 997–1019 (2013). https://doi.org/10.1007/s10959-011-0394-z
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DOI: https://doi.org/10.1007/s10959-011-0394-z