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

9423009：Sudderth摘要。 研究是抽象地计划的 赌博理论（随机控制的一种特殊形式），随机游戏，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两人零和博弈的价值函数 随机博弈还计划对一个多人班进行研究， 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，计划对某些 统计推断的基础问题。 研究是 计划如何做出最佳决策的基本问题 在不确定的情况下穿越时间抽象赌博理论 处理的问题，其中一个单一的决策者试图控制一个 过程，以达到预期的目标。在随机博弈中， 更多的决策行为来控制一个过程，可能会有相反的利益。 这类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受关注，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.