Existence of Nash equilibrium points for Markovian non-zero-sum stochastic differential games with unbounded coefficients

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2013-08-27 DOI:10.1080/17442508.2014.915973

S. Hamadène, Rui Mu

引用次数: 38

Abstract

This paper is related to non-zero-sum stochastic differential games in the Markovian framework. We show existence of a Nash equilibrium point for the game when the drift is no longer bounded and only satisfies a linear growth condition. The main tool is the notion of backward stochastic differential equations which, in our case, are multidimensional with continuous coefficient and stochastic linear growth.

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系数无界的马尔可夫非零和随机微分对策纳什平衡点的存在性

本文研究了马尔可夫框架下的非零和随机微分对策。我们证明了当漂移不再有界且仅满足线性增长条件时，博弈存在纳什平衡点。主要的工具是倒向随机微分方程的概念，在我们的例子中，它是多维的，具有连续系数和随机线性增长。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Stochastics-An International Journal of Probability and Stochastic Processes MATHEMATICS, APPLIED-STATISTICS & PROBABILITY

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastics: An International Journal of Probability and Stochastic Processes is a world-leading journal publishing research concerned with stochastic processes and their applications in the modelling, analysis and optimization of stochastic systems, i.e. processes characterized both by temporal or spatial evolution and by the presence of random effects. Articles are published dealing with all aspects of stochastic systems analysis, characterization problems, stochastic modelling and identification, optimization, filtering and control and with related questions in the theory of stochastic processes. The journal also solicits papers dealing with significant applications of stochastic process theory to problems in engineering systems, the physical and life sciences, economics and other areas. Proposals for special issues in cutting-edge areas are welcome and should be directed to the Editor-in-Chief who will review accordingly. In recent years there has been a growing interaction between current research in probability theory and problems in stochastic systems. The objective of Stochastics is to encourage this trend, promoting an awareness of the latest theoretical developments on the one hand and of mathematical problems arising in applications on the other.