There are some mathematical models(see Example2.4)and analogous results in standard martingale theorywhich can not be described by the usual fuzzy martingaletheory because of the lack of corresponding semi-orderin the...There are some mathematical models(see Example2.4)and analogous results in standard martingale theorywhich can not be described by the usual fuzzy martingaletheory because of the lack of corresponding semi-orderin the fuzzy number space(E^n,D).In this paper,asuitable semi-order in the fuzzy number space(E^n,D)and the semi-order fuzzy supermartingale and submar-tingale are introduced,the charaterlstics of semi-ordersupermartingales and submartingales,as well as theDood’s stopping theorem for them(the bounded stoppingtimes theorem and the general stopping times theoremfor a class of closable semi-order fuzzy supermartin-gales and submartingales)are established.展开更多
The authors establish a kind of inequalities for nonnegative submartingales which depend on two functions ψ and ψ, and obtain the equivalent conditions for Φ and ψ such that this kind of inequalities holds. In t...The authors establish a kind of inequalities for nonnegative submartingales which depend on two functions ψ and ψ, and obtain the equivalent conditions for Φ and ψ such that this kind of inequalities holds. In the caseΦ=ψ ε△2, it is proved that this necessary and sufficient condition is equivalent to qΦ >1.展开更多
In this note, we study inequality and limit theory under sublinear expectations. We mainly prove Doob＇s inequality for submartingale and Kolmogrov＇s inequality. By Kolmogrov＇s inequality, we obtain a special versio...In this note, we study inequality and limit theory under sublinear expectations. We mainly prove Doob＇s inequality for submartingale and Kolmogrov＇s inequality. By Kolmogrov＇s inequality, we obtain a special version of Kolmogrov＇s law of large numbers. Finally, we present a strong law of large numbers for independent and identically distributed random variables under one-order type moment condition.展开更多
文摘There are some mathematical models(see Example2.4)and analogous results in standard martingale theorywhich can not be described by the usual fuzzy martingaletheory because of the lack of corresponding semi-orderin the fuzzy number space(E^n,D).In this paper,asuitable semi-order in the fuzzy number space(E^n,D)and the semi-order fuzzy supermartingale and submar-tingale are introduced,the charaterlstics of semi-ordersupermartingales and submartingales,as well as theDood’s stopping theorem for them(the bounded stoppingtimes theorem and the general stopping times theoremfor a class of closable semi-order fuzzy supermartin-gales and submartingales)are established.
文摘The authors establish a kind of inequalities for nonnegative submartingales which depend on two functions ψ and ψ, and obtain the equivalent conditions for Φ and ψ such that this kind of inequalities holds. In the caseΦ=ψ ε△2, it is proved that this necessary and sufficient condition is equivalent to qΦ >1.
基金Supported in part by the National Natural Science Foundation of China under Grant No.11371191Jiangsu Province Basic Research Program(Natural Science Foundation)under Grant No.BK2012720
文摘In this note, we study inequality and limit theory under sublinear expectations. We mainly prove Doob＇s inequality for submartingale and Kolmogrov＇s inequality. By Kolmogrov＇s inequality, we obtain a special version of Kolmogrov＇s law of large numbers. Finally, we present a strong law of large numbers for independent and identically distributed random variables under one-order type moment condition.
