Mathematical Sciences: Abstract Gambling Theory, Stochastic Games, and Statistical Inference

9423009：突发事件研究计划在抽象赌博理论（随机控制的一个特殊公式），随机游戏，和贝叶斯统计的基础。部分研究旨在更好地理解一种新算法，该算法可用于计算赌博理论中的最优奖励函数，也可用于计算一大类二人零和随机博弈的价值函数。研究还计划在一类多人，非合作博弈，可用于研究货币和金融机构的理论问题。最后，对统计推理基础中的若干问题进行了研究规划。计划研究的基本问题是如何在存在不确定性的情况下，随着时间的推移做出最佳决策。抽象赌博理论处理的问题是单个决策者试图控制一个过程以达到预期目标。在随机博弈中，两个或两个以上的决策控制一个过程，可能有相反的利益。这些问题的数学理论是相当技术性的，但解决方案在许多领域都很有趣，包括商业、经济和运筹学。

9423009: Sudderth Abstract. Research is planned in abstract gambling theory (a particular formulation of stochastic control), stochastic games, and the foundations of Bayesian statistics. Part of the research aims for a better understanding of a new algorithm which can be used to calculate the optimal reward function in gambling theory and also to calculate the value function for a large class of two-person, zero-sum stochastic games. Research is also planned on a class of many-person, noncooperative games that can be used to study questions in the theory of money and financial institutions. Finally, research is planned on certain problems in the foundations of statistical inference. Research is planned on fundamental questions about how to make optimal decisions through time in the presence of uncertainty. Abstract gambling theory treats problems in which a single decision maker seeks to control a process so as to reach a desired objective. In stochastic games, two or more decision act to control a process and may have opposing interests. The mathematical theory of such problems is quite technical, but solutions are of interest in many areas including business, economics and operations research.