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Stochastic comparison and preservation of positive correlations for Lévy-type processes

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Abstract

The stochastic comparison and preservation of positive correlations for Lévy-type processes on ℝd are studied under the condition that Lévy measure ν satisfies ∫{0<|z|≤1}|z||ν(x, dz) − ν(x, d(−z))| < ∞, x ∈ ℝd, while the sufficient conditions and necessary ones for them are obtained. In some cases the conditions for stochastic comparison are not only sufficient but also necessary.

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Authors and Affiliations

  1. Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, P. R. China

    Jie Ming Wang

  2. School of Mathematical Sciences and Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing, 100875, P. R. China

    Jie Ming Wang

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  1. Jie Ming Wang
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Correspondence to Jie Ming Wang.

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Supported in part by Creative Research Group Fund of the National Natural Science Foundation of China (No. 10121101) and by the “985” Project from the Ministry of Education in China

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Wang, J.M. Stochastic comparison and preservation of positive correlations for Lévy-type processes. Acta. Math. Sin.-English Ser. 25, 741–758 (2009). https://doi.org/10.1007/s10114-009-7670-1

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  • DOI: https://doi.org/10.1007/s10114-009-7670-1

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