模糊值二人零和对策的Nash均衡策略

我们将在Ramik定义的模糊最大序关系基础上研究模糊环境中的二人零和对策。在非对称模糊数基础上,引入模糊环境中的几种Nash均衡策略,讨论各种均衡策略存在的充要条件。并引入含参变量确定性矩阵对策及其均衡策略的概念,讨论含参变量确定性矩阵对策的Nash均衡策略和模糊值矩阵对策的均衡策略的关系。     

Discrete semi-stable distributions

The purpose of this paper is to introduce and study the concepts of discrete semi-stability and geometric semi-stability for distributions with support inZ ₊. We offer several properties, including characterizations, of discrete semi-stable distributions. We establish that these distributions posses the property of infinite divisibility and that their probability generating functions admit canonical representations that are analogous to those of their continuous counterparts. Properties of discrete geometric semi-stable distributions are deduced from the results obtained for discrete semi-stability. Several limit theorems are established and some examples are constructed.     

Second-order linearity of the general signed-rank statistic

Let X₁,…, X_n be i.i.d. random variables symmetric about zero. Let R_i(t) be the rank of |X_i − tn^−1/2| among |X₁ − tn^−1/2|,…, |X_n − tn^−1/2| and T_n(t) = Σ_{i = 1}ⁿφ((n + 1)⁻¹R_i(t))sign(X_i − tn^−1/2). We show that there exists a sequence of random variables V_n such that sup_{0 ≤ t ≤ 1} |T_n(t) − T_n(0) − tV_n| → 0 in probability, as n → ∞. V_n is asymptotically normal.     

Semi-cooperative strategies for differential games

The paper is concerned with a non-cooperative differential game for two players. We first consider Nash equilibrium solutions in feedback form. In this case, we show that the Cauchy problem for the value functions is generically ill-posed. Looking at vanishing viscosity approximations, one can construct special solutions in the form of chattering controls, but these also appear to be unstable. In the second part of the paper we propose an alternative semi-cooperative pair of strategies for the two players, seeking a Pareto optimum instead of a Nash equilibrium. In this case, we prove that the corresponding Hamiltonian system for the value functions is always weakly hyperbolic.Revised: May 2004     

A Projected Gradient Method for Vector Optimization Problems

Vector optimization problems are a significant extension of multiobjective optimization, which has a large number of real life applications. In vector optimization the preference order is related to an arbitrary closed and convex cone, rather than the nonnegative orthant. We consider extensions of the projected gradient gradient method to vector optimization, which work directly with vector-valued functions, without using scalar-valued objectives. We provide a direction which adequately substitutes for the projected gradient, and establish results which mirror those available for the scalar-valued case, namely stationarity of the cluster points (if any) without convexity assumptions, and convergence of the full sequence generated by the algorithm to a weakly efficient optimum in the convex case, under mild assumptions. We also prove that our results still hold when the search direction is only approximately computed.     

Global weak solutions to the Nordström-Vlasov system

The Nordström-Vlasov system is a Lorentz invariant model for a self-gravitating collisionless gas. We establish suitable a priori bounds on the solutions of this system, which together with energy estimates and the smoothing effect of “momentum averaging” yield the existence of global weak solutions to the corresponding initial value problem. In the process we improve the continuation criterion for classical solutions which was derived recently. The weak solutions are shown to preserve mass.     

Weak and Strong Solutions for the Stokes Approximation of Non-homogeneous Incompressible Navier-Stokes Equations

In this paper,the Dirichlet problem of Stokes approximate of non-homogeneous incompressibleNavier-Stokes equations is studied.It is shown that there exist global weak solutions as well as global andunique strong solution for this problem,under the assumption that initial density ρ_0(x)is bounded away from0 and other appropriate assumptions(see Theorem 1 and Theorem 2).The semi-Galerkin method is applied toconstruct the approximate solutions and a prior estimates are made to elaborate upon the compactness of theapproximate solutions.     

Second order Runge–Kutta methods for Stratonovich stochastic differential equations

The weak approximation of the solution of a system of Stratonovich stochastic differential equations with a m–dimensional Wiener process is studied. Therefore, a new class of stochastic Runge–Kutta methods is introduced. As the main novelty, the number of stages does not depend on the dimension m of the driving Wiener process which reduces the computational effort significantly. The colored rooted tree analysis due to the author is applied to determine order conditions for the new stochastic Runge–Kutta methods assuring convergence with order two in the weak sense. Further, some coefficients for second order stochastic Runge–Kutta schemes are calculated explicitly. AMS subject classification (2000)  65C30, 65L06, 60H35, 60H10