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991.
S. Ramasubramanian 《Applied Mathematics and Optimization》2007,56(3):312-342
We consider a network of d companies (insurance companies, for example) operating under a treaty to diversify risk. Internal and external borrowing
are allowed to avert ruin of any member of the network. The amount borrowed to prevent ruin is viewed upon as control. Repayment
of these loans entails a control cost in addition to the usual costs. Each company tries to minimize its repayment liability.
This leads to a d -person differential game with state space constraints. If the companies are also in possible competition a Nash equilibrium
is sought. Otherwise a utopian equilibrium is more appropriate. The corresponding systems of HJB equations and boundary conditions
are derived. In the case of Nash equilibrium, the Hamiltonian can be discontinuous; there are d interlinked control problems with state constraints; each value function is a constrained viscosity solution to the appropriate
discontinuous HJB equation. Uniqueness does not hold in general in this case. In the case of utopian equilibrium, each value
function turns out to be the unique constrained viscosity solution to the appropriate HJB equation. Connection with Skorokhod
problem is briefly discussed. 相似文献
992.
993.
The paper outlines an approach to constructing a mathematical model of moving mechanical systems under uncertainty. Generalized
fuzzy differential equations are used to prove that the model is mathematically correct. The motion of a control oscillator
under uncertainty is considered as an example
__________
Translated from Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 108–119, October 2007. 相似文献
994.
Jiongmin Yong 《Applied Mathematics and Optimization》1994,29(3):243-261
In this paper we are concerned with zero-sum differential games with impulse controls, as well as continuous and switching controls. The motivation is optimal impulse control problems with disturbances. The main result is the existence of the value function of the game. Our approach is the theory of viscosity solutions for Hamilton-Jacobi equations.Part of this paper was done while the author was a visiting scholar at INRIA, Sophia-Antipolis, France. This work was also partially supported by the Chinese NSF, the Chinese State Education Commission Science Foundation, and the Fok Ying Tung Education Foundation. 相似文献
995.
N. Parhi P. Das 《数学物理学报(B辑英文版)》1998,(1)
1IntroductionInthispaperwedealwithoscillatoryandnonoscillatorybehaviourofsolutionsofnonlinearthirdorderdifferentialequationsoftheformwherea,b,cEC([er,co),R),rrER,fEC(R,R)suchthatac2P>0fory/0and7>0isaquotientofoddintegers.From"Theoryofequations"tsee[1],itfollowsthattheequationwithconstantcoefficientsMoreover,allnonoscillatorysolutionsof(1.3)tendtozeroifandonlyifequatioll(l.3)hasanoscillatorysolution.Theseobservationsarefoundtobetruetoalargeextentformoregeneralequationsoftheformwherealb,cE… 相似文献
996.
997.
本文研究具有Dirichlet边界条件的稳态半导体模型,在净复合率R≠0时,对N维半导体方程,论证了奇异摄动问题的解在H^1中弱收敛于退化问题的解;对一维半导体模型,进一步证明了解在H^1中强收敛。 相似文献
998.
P. Cardaliaguet M. Quincampoix P. Saint-Pierre 《Applied Mathematics and Optimization》1997,36(1):21-42
We study optimal times to reach a given closed target for controlled systems with a state constraint. Our goal is to characterize
these optimal time functions in such a way that it is possible to compute them numerically and we do not need to compute trajectories
of the controlled system. In this paper we provide new results using viability theory. This allows us to study optimal time
functions free from the controllability assumptions classically made in the partial differential equations approach. 相似文献
999.
本文研究Meleard-Roelly(1992,1993)和Metivier(1987)构造的带交互作用的测度值分枝过程的状态性质.我们证明在自然假设下该过程关于Lebesgue测度是绝对连续的,其密度有连续修正且满足一个随机偏微分方程. 相似文献
1000.
实Clifford分析中六类拟Bochner-Martinelli型高阶奇异积分的几个问题 总被引:10,自引:0,他引:10
本文借助于Hadamard关于高阶奇异积分有限部分的思想,研究关于实 Clifford分析中六个类型(含一个奇点或二个奇点的)拟Bochner-Martinelli型高阶奇异积分的归纳定义、Hadamard主值的存在性、递推公式、计算公式、微分公式、Poincare-Bertrand置换公式以及拟B-M型高阶奇异积分的Holder连续性等问题.这些问题是研究单、多元复分析的学者们在研究奇异积分时,通常要涉及到的几个问题. 相似文献