摘要
由非线性期望诱导出一类容度,对这类容度的性质进行了研究。为了更好地刻画容度的特点,提出了容度的弱二次交替性的概念。利用非线性期望的相关性质分别研究了容度的弱二次交替、次二次交替与二次交替的性质。对奇的非线性期望算子给出了一个定理,使得3个性质是等价的。
A class of capacity was induced by the nonlinear expectations, and the properties of this capacity were stud- ied. In order to better describe the characteristics of capacity, the notion of weak-2-alternating was proposed. Then the weak-2-alternating, sub-2-alternating and 2-alternating of capacity were respectively studied by using the properties of nonlinear expectations. Final, a theorem of the odd nonlinear expectations operator was obtained, which makes these three properties to be equivalent.
出处
《山东大学学报（理学版）》
CAS
CSCD
北大核心
2012年第10期59-63,69,共6页
Journal of Shandong University(Natural Science)
基金
国家自然科学基金资助项目(10971220)
全国优秀博士学位论文作者专项基金资助项目(200919)
中央高校基本科研业务费专项资金资助项目(2010LKSX04)
关键词
非线性期望
容度
二次交替
次二次交替
弱二次交替
nonlinear expectations
capacity
2-alternating
sub-2-alternating
weak-2-alternating
