Stochastic Comparison for Lévy-Type Processes

Jie Ming Wang

doi:10.1007/s10959-011-0394-z

Stochastic Comparison for Lévy-Type Processes

Jie Ming Wang^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

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 {νⁿ}_n≥1 different from the one in Wang (Acta Math. Sin. Engl. Ser. 25:741-758, 2009) to approach the Lévy measure ν.

Original language	English
Pages (from-to)	997-1019
Number of pages	23
Journal	Journal of Theoretical Probability
Volume	26
Issue number	4
DOIs	https://doi.org/10.1007/s10959-011-0394-z
Publication status	Published - Dec 2013

Keywords

Lévy-type processes
Stochastic comparison
Stochastic monotonicity

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10.1007/s10959-011-0394-z

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abstract = "The main goal of this paper is to establish necessary and sufficient conditions for stochastic comparison of two general L{\'e}vy-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 L{\'e}vy measures {νn}n≥1 different from the one in Wang (Acta Math. Sin. Engl. Ser. 25:741-758, 2009) to approach the L{\'e}vy measure ν.",

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AB - 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 {νn}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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KW - Stochastic monotonicity

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Stochastic Comparison for Lévy-Type Processes

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Keywords

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