Modeling and Simulation of Stochastic Systems

该研究计划涉及涉及不确定性（随机系统）的复杂系统的模拟和优化。随机建模和数值模拟现在是科学，工程，管理和其他几个领域的主要工具。仿真通常是处理复杂系统的真实模型的唯一实用工具，这些复杂系统通常是动态的，随机的和非线性的。建立具有充分代表性的随机仿真模型，设计高效可靠的仿真方法，并利用仿真来优化这些系统中的决策/操作策略，是具有巨大实际意义的任务，但仍然非常具有挑战性。我的目标是从理论观点（例如，算法的收敛性分析和随机数生成器结构的数学分析）和实践观点（经验实验，软件实现和适应特定的现实生活应用）贡献新的想法和方法来应对这些挑战。我从事一般方法学以及各种领域的选定应用程序，如金融，风险分析，通信，可靠性和服务系统的运营管理。目前和今后五年的主要研究方向是：（1）研究和改进各种用途（模拟、游戏、彩票等）的计算机产生（伪）随机数的方法;以及计算平台（例如，（2）开发和研究用于多变量集成和优化的随机化准蒙特卡罗（RQMC）方法;（3）开发对复杂随机系统（如呼叫中心、医疗保健系统、收入管理系统和其他类型的运营管理系统）建模的更现实的方法;（4）设计用于仿真（包括稀有事件仿真）的效率改进（方差减小）方法;（5）开发用于运营管理中的决策的基于随机仿真的优化方法。

This research program concerns the simulation and optimization of complex systems that involve uncertainty (stochastic systems). Stochastic modeling and numerical simulation are now primary tools in science, engineering, management, and several other areas. Simulation is often the only practical tool to deal with realistic models of complex systems, which are typically dynamic, stochastic, and nonlinear. Building sufficiently representative stochastic simulation models, designing efficient and reliable simulation methods, and using simulation to optimize decision/operation strategies in these systems, are tasks with enormous practical importance, but which remain very challenging. My goal is to contribute new ideas and methods to address these challenges both from theoretical viewpoints (for example, convergence analysis of algorithms and mathematical analysis of the structure of random number generators) and practical ones (empirical experimentation, software implementation, and adaptation to specific real-life applications). I work on general methodology as well as on selected applications in various fields such as finance, risk analysis, communications, reliability, and operations management in service systems. The main directions of my research, currently and over the next five years, are: (1) Study and improve the methods for generating (pseudo)random numbers by computer, for various usages (simulation, games, lotteries, etc.) and computing platforms (e.g., highly-parallel general-purpose processors with limited local memory); (2) develop and study randomized quasi-Monte Carlo (RQMC) methods for multivariate integration and optimization; (3) develop more realistic ways of modeling complex stochastic systems such as call centers, health-care systems, revenue management systems, and other types of operations management systems; (4) design efficiency-improvement (variance reduction) methods for simulation, including rare-event simulation; (5) develop stochastic simulation-based optimization methods for decision making in operations management.