Under the Lipschitz assumption and square integrable assumption on g, the author proves that Jensen＇s inequality holds for backward stochastic differential equations with generator g if and only if g is independent o...Under the Lipschitz assumption and square integrable assumption on g, the author proves that Jensen＇s inequality holds for backward stochastic differential equations with generator g if and only if g is independent of y, g（t, 0）≡ 0 and g is super homogeneous with respect to z. This result generalizes the known results on Jensen＇s inequality for gexpectation in [4, 7-9].展开更多
Briand et al. gave a counterexample showing that given g, Jensen's inequality for g-expectation usually does not hold in general This paper proves that Jensen's inequality for g-expectation holds in general if...Briand et al. gave a counterexample showing that given g, Jensen's inequality for g-expectation usually does not hold in general This paper proves that Jensen's inequality for g-expectation holds in general if and only if the generator g (t, z) is super-homogeneous in z. In particular, g is not necessarily convex in z.展开更多
Classical Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of random variables are basic tools for studying the strong laws of large numbers.In this paper,motived by the notion of indepen...Classical Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of random variables are basic tools for studying the strong laws of large numbers.In this paper,motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng(2008),we introduce the concept of negative dependence of random variables and establish Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of negatively dependent random variables under the sub-linear expectations.As an application,we show that Kolmogorov's strong law of larger numbers holds for independent and identically distributed random variables under a continuous sub-linear expectation if and only if the corresponding Choquet integral is finite.展开更多
We first present, by using exclusivity principle, a brief proof of the complementarity principle： the sum of squared expectation values of dichotomic （5：1） mutually complementary observables can not be greater tha...We first present, by using exclusivity principle, a brief proof of the complementarity principle： the sum of squared expectation values of dichotomic （5：1） mutually complementary observables can not be greater than 1. Then we prove that the complementarity principle yields tight quantum bounds of violations of N-qubit Svetlichny＇s inequalities. This result not only demonstrates that exclusivity principle can give tight quantum bound for certain type of genuine multipartite correlations, but also illustrates the subtle relationship between quantum complementarity and quantum genuine multipartite correlations.展开更多
基金supported by the Fundamental Research Funds for the Central Universities (Grant Nos.2019CDXYST00162018CDXYST0024)+4 种基金the China Scholarship Council (Grant No.201606055028)the National Natural Science Foundation of China (Grant No.11671060)the MOE Project of Humanities and Social Sciences on the West and the Border Area (Grant Nos.20XJC91000114XJC910001)Chongqing Key Laboratory of Analytic Mathematics and Applications
基金Project supported by the National Natural Science Foundation of China (No.10325101)the Science Foundation of China University of Mining and Technology.
文摘Under the Lipschitz assumption and square integrable assumption on g, the author proves that Jensen＇s inequality holds for backward stochastic differential equations with generator g if and only if g is independent of y, g（t, 0）≡ 0 and g is super homogeneous with respect to z. This result generalizes the known results on Jensen＇s inequality for gexpectation in [4, 7-9].
基金Project supported by the National Natural Science Foundation of China (No.10131030)
文摘Briand et al. gave a counterexample showing that given g, Jensen's inequality for g-expectation usually does not hold in general This paper proves that Jensen's inequality for g-expectation holds in general if and only if the generator g (t, z) is super-homogeneous in z. In particular, g is not necessarily convex in z.
基金supported by National Natural Science Foundation of China(Grant No.11225104)the Fundamental Research Funds for the Central Universities
文摘Classical Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of random variables are basic tools for studying the strong laws of large numbers.In this paper,motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng(2008),we introduce the concept of negative dependence of random variables and establish Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of negatively dependent random variables under the sub-linear expectations.As an application,we show that Kolmogorov's strong law of larger numbers holds for independent and identically distributed random variables under a continuous sub-linear expectation if and only if the corresponding Choquet integral is finite.
文摘We first present, by using exclusivity principle, a brief proof of the complementarity principle： the sum of squared expectation values of dichotomic （5：1） mutually complementary observables can not be greater than 1. Then we prove that the complementarity principle yields tight quantum bounds of violations of N-qubit Svetlichny＇s inequalities. This result not only demonstrates that exclusivity principle can give tight quantum bound for certain type of genuine multipartite correlations, but also illustrates the subtle relationship between quantum complementarity and quantum genuine multipartite correlations.
