JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (8): 1-9.doi: 10.6040/j.issn.1671-9352.0.2016.312

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Jensens inequality, moment inequality and law of large numbers for weighted g-expectation

JIANG Long, CHEN Min   

  1. College of Sciences, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China
  • Received:2016-06-29 Online:2016-08-20 Published:2016-08-08

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Abstract: We propose the notion of weighted g-expectation ελg ［·］ based on g-expectation. We prove that if the generator g is non-increasing with respect to y and positive-homogeneous with respect to (y,z), the moment inequality for weighted g-expectation holds in general. When λ≥1/2 and the generator g is independent of y, we establish Jensens inequality for weighted g-expectation when g is super-homogeneous with respect to z, and we establish the law of large numbers for weighted g-expectation when g is sublinear with respect to z.

Key words: weighted g-expectation, Jensens inequality, law of large numbers, g-expectation, moment inequality

CLC Number: 

  • O211
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