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This paper is focused on the investigation of the Walrasian economic equilibrium problem involving utility functions. The
equilibrium problem is here reformulated by means of a quasi-variational inequality problem. Our goal is to give an existence
result without assuming strong monotonicity conditions. To this end, we make use of a perturbation procedure. In particular,
we will consider suitable perturbed utility functions whose gradient satisfies a strong monotonicity condition and whose associated
equilibrium problem admits a solution. Then, we will prove that the limit solution solves the unperturbed problem. We stress
out that our result allows us to consider a wide class of utility functions in which the Walrasian equilibrium problem may
be solved. 相似文献
3.
James D. E. Grant 《Annales Henri Poincare》2011,12(5):965-985
Motivated by recent work of Choquet-Bruhat et al. (Class Quantum Gravity 26(135011), 22, 2009), we prove monotonicity properties and comparison results for the area of slices of the null cone of a point in a Lorentzian
manifold. We also prove volume comparison results for subsets of the null cone analogous to the Bishop–Gromov relative volume
monotonicity theorem and Günther’s volume comparison theorem. We briefly discuss how these estimates may be used to control
the null second fundamental form of slices of the null cone in Ricci-flat Lorentzian four-manifolds with null curvature bounded
above. 相似文献
4.
In this paper we introduce a new logarithmic entropy functional for the linear heat equation on complete Riemannian manifolds and prove that it is monotone decreasing on complete Riemannian manifolds with nonnegative Ricci curvature. Our results are simpler version, without Ricci flow, of R.-G. Ye’s recent result (arXiv:math.DG/0708.2008). As an application, we apply the monotonicity of the logarithmic entropy functional of heat kernels to characterize Euclidean space. 相似文献
5.
We develop a very general operator-valued functional calculus for operators with an calculus. We then apply this to the joint functional calculus of two sectorial operators when one has an calculus. Using this we prove theorem of Dore-Venni type on sums of sectorial operators and apply our results to the problem
of maximal regularity. Our main assumption is the R-boundedness of certain sets of operators, and therefore methods from the
geometry of Banach spaces are essential here. In the final section we exploit the special Banach space structure of spaces and spaces, to obtain some more detailed results in this setting.
Received: 3 July 2000 / Revised version: 31 January 2001 / Published online: 23 July 2001 相似文献
6.
We show that the types of the witnesses in the Herbrand functional interpretation can be simplified, avoiding the use of “sets of functionals” in the interpretation of implication and universal quantification. This is done by presenting an alternative formulation of the Herbrand functional interpretation, which we show to be equivalent to the original presentation. As a result of this investigation we also strengthen the monotonicity property of the original presentation, and prove a monotonicity property for our alternative definition. 相似文献
7.
Utility function properties as monotonicity and concavity play a fundamental role in reflecting a decision-maker’s preference structure. These properties are usually characterized via partial derivatives. However, elicitation methods do not necessarily lead to twice-differentiable utility functions. Furthermore, while in a single-attribute context concavity fully reflects risk aversion, in multiattribute problems such correspondence is not one-to-one. We show that Tsetlin and Winkler’s multivariate risk attitudes imply ultramodularity of the utility function. We demonstrate that geometric properties of a multivariate utility function can be successfully studied by utilizing an integral function expansion (functional ANOVA). The necessary and sufficient conditions under which monotonicity and/or ultramodularity of single-attribute functions imply the monotonicity and/or ultramodularity of the corresponding multiattribute function under additive, preferential and mutual utility independence are then established without reliance on the utility function differentiability. We also investigate the relationship between the presence of interactions among the attributes of a multiattribute utility function and the decision-maker’s multivariate risk attitudes. 相似文献
8.
We introduce and study a new concept of a weak elliptic equation for measures on infinite dimensional spaces. This concept
allows one to consider equations whose coefficients are not globally integrable. By using a suitably extended Lyapunov function
technique, we derive a priori estimates for the solutions of such equations and prove new existence results. As an application,
we consider stochastic Burgers, reaction-diffusion, and Navier-Stokes equations and investigate the elliptic equations for
the corresponding invariant measures. Our general theorems yield a priori estimates and existence results for such elliptic
equations. We also obtain moment estimates for Gibbs distributions and prove an existence result applicable to a wide class
of models.
Received: 23 January 2000 / Revised version: 4 October 2000 / Published online: 5 June 2001 相似文献
9.
François Coquet Ying Hu Jean Mémin Shige Peng 《Probability Theory and Related Fields》2002,123(1):1-27
From a general definition of nonlinear expectations, viewed as operators preserving monotonicity and constants, we derive,
under rather general assumptions, the notions of conditional nonlinear expectation and nonlinear martingale. We prove that
any such nonlinear martingale can be represented as the solution of a backward stochastic equation, and in particular admits
continuous paths. In other words, it is a g-martingale.
Received: 2 February 2000 / Revised version: 1 June 2001 / Published online: 13 May 2002 相似文献
10.
We study a phase-field-crystal model described by a free energy functional involving second-order derivatives of the order parameter in a periodic setting and under a fixed mass constraint. We prove a $$\Gamma $$-convergence result in an asymptotic thin-film regime leading to a reduced two-dimensional model. For the reduced model, we prove necessary and sufficient conditions for the global minimality of the uniform state. We also prove similar results for the Ohta–Kawasaki model. 相似文献
11.
H. Z. Munthe-Kaas G. R. W. Quispel A. Zanna 《Foundations of Computational Mathematics》2001,1(3):297-324
The polar decomposition, a well-known algorithm for decomposing real matrices as the product of a positive semidefinite matrix
and an orthogonal matrix, is intimately related to involutive automorphisms of Lie groups and the subspace decomposition they
induce. Such generalized polar decompositions, depending on the choice of the involutive automorphism σ , always exist near the identity although frequently they can be extended to larger portions of the underlying group.
In this paper, first of all we provide an alternative proof to the local existence and uniqueness result of the generalized
polar decomposition. What is new in our approach is that we derive differential equations obeyed by the two factors and solve
them analytically, thereby providing explicit Lie-algebra recurrence relations for the coefficients of the series expansion.
Second, we discuss additional properties of the two factors. In particular, when σ is a Cartan involution, we prove that the subgroup factor obeys similar optimality properties to the orthogonal polar factor
in the classical matrix setting both locally and globally, under suitable assumptions on the Lie group G .
September 12, 2000. Final version received: April 16, 2001. 相似文献
12.
This paper aims at solving a multidimensional backward stochastic differential equation (BSDE) whose generator g satisfies a weak monotonicity condition and a general growth condition in y. We first establish an existence and uniqueness result of solutions for this kind of BSDEs by using systematically the technique of the priori estimation, the convolution approach, the iteration, the truncation and the Bihari inequality. Then, we overview some assumptions related closely to the monotonieity condition in the literature and compare them in an effective way, which yields that our existence and uniqueness result really and truly unifies the Mao condition in y and the monotonieity condition with the general growth condition in y, and it generalizes some known results. Finally, we prove a stability theorem and a comparison theorem for this kind of BSDEs, which also improves some known results. 相似文献
13.
Dinah Rosenberg Eilon Solan Nicolas Vieille 《Probability Theory and Related Fields》2001,119(3):433-451
We study stopping games in the setup of Neveu. We prove the existence of a uniform value (in a sense defined below), by allowing
the players to use randomized strategies. In constrast with previous work, we make no comparison assumption on the payoff
processes. Moreover, we prove that the value is the limit of discounted values, and we construct ε-optimal strategies.
Received: 10 May 1999 / Revised version: 18 May 2000 / Published online: 15 February 2001 相似文献
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Tobias Holck Colding 《Acta Mathematica》2012,209(2):229-263
We prove three new monotonicity formulas for manifolds with a lower Ricci curvature bound and show that they are connected to rate of convergence to tangent cones. In fact, we show that the derivative of each of these three monotone quantities is bounded from below in terms of the Gromov?CHausdorff distance to the nearest cone. The monotonicity formulas are related to the classical Bishop?CGromov volume comparison theorem and Perelman??s celebrated monotonicity formula for the Ricci flow. We will explain the connection between all of these. Moreover, we show that these new monotonicity formulas are linked to a new sharp gradient estimate for the Green function that we prove. This is parallel to the fact that Perelman??s monotonicity is closely related to the sharp gradient estimate for the heat kernel of Li?CYau. In [CM4] one of the monotonicity formulas is used to show uniqueness of tangent cones with smooth cross-sections of Einstein manifolds. Finally, there are obvious parallelisms between our monotonicity and the positive mass theorem of Schoen?CYau and Witten. 相似文献
16.
Consider uncertain alternatives for which an event has two consequences (binary gambles, “gambles” for short) and over them
an operation of joint receipt which need not be closed and may be non-commutative. The two structures are linked by a distributivity
property called segregation and a preference order. Utility functions order nonnegative numbers to consequences and gambles.
Utility representations describe how the utility of a gamble depends on the utilities of consequences and on the “weight”
of the event (a number in [0,1], depending on the event). Functional characterizations give necessary and sufficient conditions,
often in form of functional equations, for certain properties of representations. We first give a functional characterization
of the often postulated event commutativity stating that two events can be interchanged in special composite gambles where
one outcome is a consequence but the other is itself a gamble. A utility representation is separable if it is multiplicative
for gambles with one consequence having 0 utility. We give three more specific characterizations of separable representations
by segregation, by homogeneity and event commutativity, and by homogeneity and segregation, and show that in the last case
event commutativity follows.
Received 10 August 2001; in revised form 6 November 2001 相似文献
17.
R. Monneau 《Journal of Geometric Analysis》2003,13(2):359-389
We study the obstacle problem in two dimensions. On the one hand we improve a result of L.A. Caffarelli and N.M. Rivière:
we state that every connected component of the interior of the coincidence set has at most N
0
singular points, where N
0
is only dependent on some geometric constants. Moreover, if the component is small enough, then this component has at most
two singular points. On the other hand, we prove in a simple case a conjecture of D.G. Schaeffer on the generic regularity
of the free boundary: for a family of obstacle problems in two dimensions continuously indexed by a parameter λ, the free
boundary of the solution uλ is analytic for almost every λ. Finally we present a new monotonicity formula for singular points.
Dedicated to Henri Berestycki and Alexis Bonnet. 相似文献
18.
本文运用Levy提出的变换研究需求可变性降低对风险偏好零售商的库存决策、销售努力决策和期望效用的影响,用均值CVaR刻画零售商的风险偏好特性,它包括风险厌恶、风险追求,也具有损失规避的特性。首先,运用该变换定量刻画需求可变性的降低,证明该变换蕴含经典随机占优中的割准则序和二阶随机占优等。其次,给出系统的最优订货量、最优期望效用和最优销售努力水平,得到它们关于风险偏好系数的单调性,并给出降低需求可变性对期望效用的影响。第三,针对风险中性、风险厌恶(最大化CVaR)和风险追求(最小化CVaR)这三种特殊情况得到相应的结果,并给出企业在库存决策和促销决策的管理启示。最后,通过数值例子验证了得到的研究结果并给出相应的管理启示。 相似文献
19.
We prove some new pathwise comparison results for single class stochastic fluid networks. Under fairly general conditions,
monotonicity with respect to the (state- and time-dependent) routing matrices is shown. Under more restrictive assumptions,
monotonicity with respect to the service rates is shown as well. We conclude by using the comparison results to establish
a moment bound, a stability result for stochastic fluid networks with Lévy inputs, and a comparison result for multi-class
GPS networks. 相似文献
20.
Mauro Nacinovich Rosanna Schianchi 《Calculus of Variations and Partial Differential Equations》2002,15(2):203-214
In this paper we prove a lower semicontinuity result for a functional , defined on a class of bounded subsets of with a piecewise boundary, with respect to the -convergence of the sets. The functional depends on the curvature of in a linear way and contains a penalizing term which prevents the appearance of thin sets in the symmetric difference , where in an -approximating sequence of .
Received: 3 January 2001 / Accepted: 11 May 2001 / Published online: 19 October 2001 相似文献