Mathematical Sciences: Complex Stochastic Systems

该奖项将支持马尔可夫过程、随机分析、空间点过程、无限记忆链、大偏差理论、分支过程和随机控制领域的研究项目。对马尔可夫过程的研究将集中在被限制在自然状态空间的一个子集上的过程，与群体遗传学相关的测量值过程，以及随机网络模型。研究随机微分方程的模拟和逼近方法将强调逼近误差的渐近性。对大偏差的研究将包括进一步的理论发展以及模拟和假设检验的应用。将探讨分支过程在光纤通信系统中出现的问题中的应用。一般随机控制问题的理论发展将包括近似方法和马尔可夫控制和最优奇异控制的存在定理。随机控制的应用将集中在存在标记缺陷的消耗模型上。该奖项将支持马尔可夫过程、随机分析、空间点过程和随机控制领域的研究项目。这项研究属于概率论的范围，但它的动机和将被应用于各种领域的问题：人口遗传学，工程和金融。

This award will support a research program in the areas of Markov processes, stochastic analysis, spatial point processes, chains with infinite memory, large deviation theory, branching processes, and stochastic control. Work on Markov processes will focus on processes constrained to a subset of their natural state space, measure-valued processes related to population genetics, and models of stochastic networks. A study of simulation and approximation methods for stochastic differential equations will emphasize asymptotics for the error in approximation. Work on large deviations will include both further theoretical developments and applications to simulation and hypothesis testing. Applications of branching processes to problems arising in fiber optic communication systems will be explored. Theoretical development for general stochastic control problems will include approximation methodology and existence theorems for Markov controls and optimal singular controls. Applications of stochastic control will focus on consumption models in the presence of mark imperfections. This award will support a research program in the areas of Markov processes, stochastic analysis, spatial point processes, and stochastic control. This research falls within the area of probability theory, but is motivated and will be applied to problems in a variety of fields: population genetics, engineering, and finance.