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

9423009：首德摘要。计划在抽象博彩理论(随机控制的一种特殊形式)、随机博弈和贝叶斯统计学的基础方面进行研究。部分研究的目的是为了更好地理解一种新的算法，该算法可以用来计算赌博理论中的最优回报函数，也可以计算一大类两人零和随机对策的值函数。还计划对一类多人非合作博弈进行研究，这种博弈可以用来研究货币和金融机构理论中的问题。最后，对统计推理基础上的若干问题进行了研究。研究计划是关于如何在存在不确定性的情况下通过时间做出最佳决策的基本问题。抽象博彩理论处理的是单个决策者试图控制一个过程以达到预期目标的问题。在随机博弈中，两个或多个决策行为控制一个过程，可能具有相反的利益。这类问题的数学理论相当技术性，但解决方案在许多领域都很有趣，包括商业、经济学和运筹学。

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.