共查询到20条相似文献,搜索用时 31 毫秒
1.
Cheng HU 《数学年刊B辑(英文版)》2018,39(5):791-804
This paper deals with strong laws of large numbers for sublinear expectation under controlled 1st moment condition. For a sequence of independent random variables, the author obtains a strong law of large numbers under conditions that there is a control random variable whose 1st moment for sublinear expectation is finite. By discussing the relation between sublinear expectation and Choquet expectation, for a sequence of i.i.d random variables, the author illustrates that only the finiteness of uniform 1st moment for sublinear expectation cannot ensure the validity of the strong law of large numbers which in turn reveals that our result does make sense. 相似文献
2.
In this note, the authors survey the existing convergence results
for random variables under sublinear expectations, and prove some
new results. Concretely, under the assumption that the sublinear
expectation has the monotone continuity property, the authors prove
that convergence in capacity is stronger than convergence in
distribution, and give some equivalent characterizations of
convergence in distribution. In addition, they give a dominated
convergence theorem under sublinear expectations, which may have its
own interest. 相似文献
3.
Survey on normal distributions,central limit theorem,Brownian motion and the related stochastic calculus under sublinear expectations 总被引:1,自引:0,他引:1
ShiGe Peng 《中国科学A辑(英文版)》2009,52(7):1391-1411
This is a survey on normal distributions and the related central limit theorem under sublinear expectation. We also present Brownian motion under sublinear expectations and the related stochastic calculus of Itô’s type. The results provide new and robust tools for the problem of probability model uncertainty arising in financial risk, statistics and other industrial problems. 相似文献
4.
José H. Dulá 《Mathematical Programming》1992,55(1-3):69-80
We introduce an upper bound on the expectation of a special class of sublinear functions of multivariate random variables defined over the entire Euclidean space without an independence assumption. The bound can be evaluated easily requiring only the solution of systems of linear equations thus permitting implementations in high-dimensional space. Only knowledge on the underlying distribution means and second moments is necessary. We discuss pertinent techniques on dominating general sublinear functions by using simpler sublinear and polyhedral functions and second order quadratic functions. 相似文献
5.
Strong laws of large numbers play key role in nonadditive probability theory. Recently, there are many research papers about strong laws of large numbers for independently and identically distributed (or negatively dependent) random variables in the framework of nonadditive probabilities (or nonlinear expectations). This paper introduces a concept of weakly negatively dependent random variables and investigates the properties of such kind of random variables under a
framework of nonadditive probabilities and sublinear expectations. A strong law of large numbers is also proved for weakly negatively dependent random variables under a kind of sublinear expectation as an application 相似文献
6.
Under the framework of sublinear expectation,we introduce a new type of G-Gaussian random fields,which contains a type of spatial white noise as a special case.Based on this result,we also introduce a spatial-temporal G-white noise.Different from the case of linear expectation,in which the probability measure needs to be known,under the uncertainty of probability measures,spatial white noises are intrinsically different from temporal cases. 相似文献
7.
In this note we discuss uniform integrability of random variables. In a probability space, we introduce two new notions on uniform integrability of random variables, and prove that they are equivalent to the classic one. In a sublinear expectation space, we give de La Vall\'{e}e Poussin criterion for the uniform integrability of random variables and do some other discussions. 相似文献
8.
Hong Zhang 《随机分析与应用》2013,31(6):1067-1096
In this article we take the initial step in the study of kinematics of stochastic motion under the sublinear expectation approach, (the so called G-framework). We compute, in this article, the stochastic forward/backward derivatives/drifts of some G-diffusion processes, and calculate the current and osmotic velocities. While the G-framework that we use creates a few technical difficulties, it also rewards us with nice extensions of results corresponding to the linear expectation case. 相似文献
9.
The aim of this paper is to establish a series of important properties of local Lipschitz-α mappings from a subset of a normed space into a normed space. These mappings include Lipschitz operators, Lipschitz-α operators and local Lipschitz functions. Some applications to the theory of sublinear expectation spaces are given. 相似文献
10.
Designing a majorization scheme for the recourse function in two-stage stochastic linear programming
José H. Dulá 《Computational Optimization and Applications》1993,1(4):399-414
We discuss issues pertaining to the domination from above of the second-stage recourse function of a stochastic linear program and we present a scheme to majorize this function using a simpler sublinear function. This majorization is constructed using special geometrical attributes of the recourse function. The result is a proper, simplicial function with a simple characterization which is well-suited for calculations of its expectation as required in the computation of stochastic programs. Experiments indicate that the majorizing function is well-behaved and stable. 相似文献
11.
Dmitry B. Rokhlin 《Archiv der Mathematik》2017,108(3):325-335
For a finite function class, we describe the large sample limit of the sequential Rademacher complexity in terms of the viscosity solution of a G-heat equation. In the language of Peng’s sublinear expectation theory, the same quantity equals to the expected value of the largest order statistics of a multidimensional G-normal random variable. We illustrate this result by deriving upper and lower bounds for the asymptotic sequential Rademacher complexity. 相似文献
12.
In this paper, we first study the martingale problem in a sublinear expectation space. The critical tool is the Evans–Krylov theorem on regularity properties for solutions of fully nonlinear PDEs. Based on the analysis for the martingale problem and inspired by the rough path theory, we then develop stochastic calculus with respect to a general stochastic process, and derive an Itô type formula and the integration-by-parts formula. Our framework is analytic in that it does not rely on the probabilistic concept of “independence” as in the -expectation theory. 相似文献
13.
GuangYan Jia 《中国科学A辑(英文版)》2009,52(4):785-793
In this paper, we prove that for a sublinear expectation ɛ[·] defined on L
2(Ω,), the following statements are equivalent:
Furthermore, we prove a sandwich theorem for subadditive expectation and superadditive expectation.
This work was supported by National Basic Research Program of China (973 Program) (Grant No. 2007CB814901) (Financial Risk)
and National Natural Science Foundation of China (Grant No. 10671111) 相似文献
(i) | ɛ is a minimal member of the set of all sublinear expectations defined on L 2(Ω,) |
(ii) | ɛ is linear |
(iii) | the two-dimensional Jensen’s inequality for ɛ holds. |
14.
《Operations Research Letters》2022,50(5):517-523
This paper develops and studies a feasible directions approach for the minimization of a continuous function over linear constraints in which the update directions belong to a predetermined finite set spanning the feasible set. These directions are recurrently investigated in a cyclic semi-random order, where the stepsize of the update is determined via univariate optimization. We establish that any accumulation point of this optimization procedure is a stationary point of the problem, meaning that the directional derivative in any feasible direction is nonnegative. To assess and establish a rate of convergence, we develop a new optimality measure that acts as a proxy for the stationarity condition, and substantiate its role by showing that it is coherent with first-order conditions in specific scenarios. Finally we prove that our method enjoys a sublinear rate of convergence of this optimality measure in expectation. 相似文献
15.
Yu Lian Fan 《数学学报(英文版)》2012,28(8):1597-1614
In the context of model uncertainty, we study the optimal design and the pricing of financial instruments aiming to hedge some of non-tradable risks. For the existence of model uncertainty, the preference can be represented by the robust expected utility (also called maxmin expected utility) which can be put in the framework of sublinear expectation. The problem of maximizing the issuer’s robust expected utility under the constraint imposed by the buyer can be transformed to the problem of minimizing the issuer’s convex measure under the corresponding constraint. And here the convex measure measures not only the risks but also the model uncertainties. 相似文献
16.
ABSTRACTHaving a function being a difference of sublinear functions defined on a plane, we present a formula for effective calculation of sublinear functions such that their difference is equal to the given one. Moreover, these newly calculated sublinear functions are minimal and as such unique-up-to-linear-summand. We also provide examples of such functions. 相似文献
17.
关于次线性椭圆方程正解的对称性 总被引:1,自引:0,他引:1
梅海涛 《高校应用数学学报(A辑)》1999,14(2):155-160
本文利用次线性项在零点附近的凹性和可积发表和移动平面法给出一类次线性椭圆方程正解的对称性。 相似文献
18.
In this paper, criteria are established for the existence of periodic solutions to a second order sublinear neutral differential equation. Our method is based on careful a priori estimation and continuation theorem, and our sublinear condition is an improvement of the boundedness condition in some recent results. 相似文献
19.
We show that the celebrated Farkas lemma for linear inequality systems continues to hold for separable sublinear inequality
systems. As a consequence, we establish a qualification-free characterization of optimality for separable sublinear programming
problems which include classes of robust linear programming problems. We also deduce that the Lagrangian duality always holds
for these programming problems without qualifications. 相似文献
20.
In this paper, we consider strict comparison theorems in the framework of G-expectation, which is a type of sublinear expectation associated with fully nonlinear parabolic partial differential equations. In particular, we first apply Krylov–Safonov estimates to establish the strict comparison theorem for functions from the Lipschitz class \(Lip(\Omega )\). Then we prove generalized strict comparison theorems on the enlarged space \(L_G^1(\Omega )\), which is the Banach completion of \(Lip(\Omega )\) under the G-expectation. 相似文献