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Dynamically consistent nonlinear evaluations with their generating functions in L p

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Abstract

In this paper, we study dynamically consistent nonlinear evaluations in L p (1 < p < 2). One of our aim is to obtain the following result: under a domination condition, an F t -consistent evaluation is an E g-evaluation in L p. Furthermore, without the assumption that the generating function g (t, ω, y, z) is continuous with respect to t, we provide some useful characterizations of an E g-evaluation by g and give some applications. These results include and extend some existing results.

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Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, P. R. China

    Feng Hu

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  1. Feng Hu
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Correspondence to Feng Hu.

Additional information

Supported by National Natural Science Foundation of China (Grant No. 11171179), Doctoral Program Foundation of Ministry of Education of China (Grant No. 20123705120005), Natural Science Foundation of Shandong Province of China (Grant No. ZR2012AQ009), Postdoctoral Science Foundation of China (Grant No. 2012M521301), Doctoral Foundation of Qufu Normal University (Grant No. BSQD20110128) and Youth Foundation of Qufu Normal University (Grant No. XJ201111)

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Hu, F. Dynamically consistent nonlinear evaluations with their generating functions in L p . Acta. Math. Sin.-English Ser. 29, 815–832 (2013). https://doi.org/10.1007/s10114-013-1715-1

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  • DOI: https://doi.org/10.1007/s10114-013-1715-1

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