g-期望关于凸(凹)函数的Jensen不等式

在文[8]的基础上和彭实戈提出的关于g-期望的最基本的条件下,证明了g-期望关于凸(凹)函数的Jensen不等式在一般意义下成立当且仅当g是关于(y,z)的超齐次(次齐次)生成元且不依赖于y.     

半正定(半负定)二元函数基于g-期望的Jensen不等式

彭实戈通过倒向随机微分方程引入了g-期望的概念.在关于g-期望的最基本的条件下,提出并证明了:半正定(半负定)二元函数基于g-期望的Jensen不等式在非空数集S上成立当且仅当生成元g在S上是超线性(次线性)的.     

条件g-期望的矩不等式

找到了几个使条件g-期望的矩不等式在一般意义下成立的关于g和g-期望的充分条件.     

Choquet期望,最大(最小)期望和推广的Peng’s g-期望（英文）

Choquet期望和最大(最小)期望是非线性期望,它们替代经典的数学期望被广泛地应用在经济、金融和保险中.但是,由于非线性,计算它们往往非常困难.本文首先介绍推广的Peng’s g-期望及其相关性质;然后,给出最大(最小)期望和推广的Peng’s g-期望之间的关系;最后,利用Peng’s g-期望,在一些合理假设下,得到Choquet期望和最大(最小)期望是一致的.     

g-期望的分布不变性

当g-期望具有分布不变性时,给出了g所满足的充要条件.并证明了当且仅当g为零时,g-期望其有分布不变性.     

L~p空间中随机变量的g-期望与条件g-期望

利用倒向随机微分方程的Lp解定义了Lp空间中随机变量g-期望与条件g-期望,扩张了g-期望与条件g-期望的定义空间;证明了用Lp解定义的g-期望与文[5]用算子连续扩张方法定义的一般g-期望的一致性,得到了Lp空间中随机变量的g-期望与条件g-期望的一些性质.     

Lp空间中随机变量的g-期望与条件g-期望

利用倒向随机微分方程的Lp解定义了Lp空间中随机变量g-期望与条件g-期望,扩张了g-期望与条件g-期望的定义空间;证明了用Lp解定义的g-期望与文[5]用算子连续扩张方法定义的一般g-期望的一致性,得到了Lp空间中随机变量的g-期望与条件g-期望的一些性质.     

广义齐次函数

若函数f(x,y)在其定义域G上满足恒等式 f(tx,ty)=t~nf(x,y),t>0,则称f(x,y)为n次齐次函数。把这个概念推广一下,还可以得到一类广义齐次函数,本文的目的就是对这类广义齐次函数的性质作一初步的讨论。定义.若函数f(x,y)在其定义域G上对一切t>0恒满足等式 f(tx,ty)=h(x,y)k(t)+z~mf(x,y),(1)其中h(x,y)为n次齐次函数,k(t)=t~mlnt(n=m时)或k(t)=(t~n-t~m)(n≠m时),则我们称函数f(x,y)为关于特征函数h(x,y)的m次广义齐次函数。例如,xlny+ylnx+x为关于特征函数x+y的1次广义齐次函数。而x~2+y~2+x~2y则为关于特     

Peng g- 期望下的大数定律

Peng 于1997 年通过倒向随机微分方程引入了一类性质很好的非线性数学期望, 即g- 期望. 本文中, 我们将给出Peng g- 期望下的弱大数定律与强大数定律.     

带有随机生成元的倒向随机微分方程的共单调定理

该文利用Malliavin微分的方法研究带有随机生成元的倒向随机微分方程 (简记BSDE),给出了关于比较某些BSDE的解(y,z)中z的方法, 在此基础上继续研究(y,z)的某些重要性质, 指明了当BSDE的生成元是随机的情况下,Zengjing Chen等人文章中得到的共单调定理是不成立的, 然后寻找带有随机生成元的BSDE的共单调定理成立的特殊情况, 最后研究了一类g -期望的可加性以及Choquet积分表示定理.     

Jensen's Inequality for Backward Stochastic Differential Equations

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 g-expectation in [4, 7-9].     

ON JENSEN’S INEQUALITY FOR g-EXPECTATION

Briand et al. gave a counterexample showing that given g, Jensen's inequalityfor g-expectation usually does not hold in general. This paper proves that Jensen'sinequality for g-expectation holds in general if and only if the generator g(t,z) issuper-homogeneous in z. In particular, g is not necessarily convex in z.     

一类滞后差分方程解的渐近性

考虑时滞差分方程xn－xn-1＝F（－f（xn）＋g（xn－k）），这里k是正整数，F，f，g是R→R的连续函数，F和f在R上单调增加，且对所有的u≠0，uF（u）＞0.我们证明了如果对所有的y∈R，有f（y）≥g（y）（f（y）≤g（y）），则方程的每个解趋于一个常数或－∞（∞）．进一步，如果对所有的y∈R，有f（y）≡g（y）；则方程的每个解当n→∞时趋于常数．     

Projective metabelianD-groups and Lie superalbegras

The main result of this paper shows that the projective objects in varieties of metabelian R-groups and Lie superalgebras are free. A D-group is a group in which for any element x and any natural number n there exists a unique element y such that x=yⁿ. A Lie superalgebra (resp. D-group) is metabelian if it is an extension of an abelian superalgebra (resp. D-group) by an abelian superalgebra (resp. D-group). The proof of the main result relies on the representation of projective superalgebras (resp. D-groups) in projective modules over rings that are nearly polynomial rings. Bibliography: 17 titles.Translated fromTrudy Seminara imeni I. G. Petrovskogo, No. 15, pp. 189–195.     

Sur la (-k)-demi-reconstructibilité des tournois finis

Given a tournament T, we define the dual T^* of T by T^*(x,y) = T(y,x). A tournament T′ is hemimorphic to T if it is isomorphic to T or T^*. A tournament defined on n elements is (-k-reconstructible (resp. (-k)-half-reconstructible) if it is determined up to isomorphism (resp. up to hemimorphism), by its restrictions to subsets of (n - k) elements. From [2] follows the (-k)-half-reconstructibility of finite tournaments (with n ≥ (7 + k) elements), for all k > 7. In this Note, we establish the (-k)-half-reconstructibility of finite tournaments (with n ≥ (12 + k) elements), for all k4,5,6. We then connect the problems of the (-3)- and the (−2)-half-reconstruction of these tournaments to two problems (yet open) of reconstruction. Finally, by using counterexamples of P.K. Stockmeyer [14], we show that, generally, the finite tournaments are not (-k)-half-reconstructible.     

LEFT-RIGHT BROWDER LINEAR RELATIONS AND RIESZ PERTURBATIONS

A closed linear relation T in a Banach space X is called left(resp. right) Fredholm if it is upper(resp. lower) semi Fredholm and its range(resp. null space) is topologically complemented in X. We say that T is left(resp. right) Browder if it is left(resp. right)Fredholm and has a finite ascent(resp. descent). In this paper, we analyze the stability of the left(resp. right) Fredholm and the left(resp. right) Browder linear relations under commuting Riesz operator perturbations. Recent results of Zivkovic et al. to the case of bounded operators are covered.