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Stochastic Comparison for Lévy-Type Processes

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  • Jie-Ming Wang

    (Beijing Institute of Technology)

Abstract

The main goal of this paper is to establish necessary and sufficient conditions for stochastic comparison of two general Lévy-type processes on ℝ d . 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.

Suggested Citation

  • Jie-Ming Wang, 2013. "Stochastic Comparison for Lévy-Type Processes," Journal of Theoretical Probability, Springer, vol. 26(4), pages 997-1019, December.
    • Handle: RePEc:spr:jotpro:v:26:y:2013:i:4:d:10.1007_s10959-011-0394-z
    DOI: 10.1007/s10959-011-0394-z
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    References listed on IDEAS

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    1. Keilson, Julian & Kester, Adri, 1977. "Monotone matrices and monotone Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 5(3), pages 231-241, July.
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