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

9423009：萨德斯摘要。 计划研究抽象赌博理论（随机控制的一种特殊表述）、随机博弈和贝叶斯统计基础。 该研究的部分目的是为了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两人零和随机游戏的价值函数。还计划研究一类多人非合作博弈，可用于研究货币和金融机构理论中的问题。最后，计划对统计推断基础上的某些问题进行研究。 计划研究有关如何在存在不确定性的情况下随时间做出最佳决策的基本问题。抽象赌博理论处理的是单个决策者试图控制过程以达到预期目标的问题。在随机博弈中，两个或多个决策采取行动来控制一个过程，并且可能有相反的利益。 此类问题的数学理论相当技术性，但解决方案在商业、经济学和运筹学等许多领域都很有趣。

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.