Simulation of stochastic systems

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This project concerns the simulation and optimization of complex stochastic systems (that involve uncertainty). Stochastic modeling and simulation are primary tools in science, engineering, economics, management, and several other areas. Simulation has become more attractive and less expensive than experimenting with the real systems, due to the decreasing cost of computing and the improvement in simulation methodology and software in the last decades. Simulation is often the only practical tool to deal with realistic models of complex systems, which are typically dynamic, stochastic, and nonlinear. However, designing efficient and reliable simulation methods, and using simulation to optimize decision/operation strategies in these systems, remains very difficult. Random number generators are a fundamental ingredient for stochastic simulation. They are also needed for computer games, gambling machines, and cryptology, for example. Their quality criteria differ across areas of applications, whence the need for different types of designs and for theoretical studies from different viewpoints. Quasi-Monte Carlo methods replace the vectors of random numbers used in a simulation by points that cover the space more uniformly than random points, to improve the accuracy of the simulation results. Other ways of improving efficiency include concentrating the sampling adaptively toward the most important events. My research focuses on the design and analysis of methods for: (1) random number generators for various types of applications, (2) high-dimensional numerical integration via randomized quasi-Monte Carlo, (3) improving the efficiency of simulations (e.g., by designing estimators with smaller variance) and dealing with rare events, (4) optimization of stochastic systems via simulation. These methods are applied in several areas such as finance, risk analysis, telecommunications, management, and so on. Both theoretical aspects (e.g., convergence analysis of algorithms and mathematical analysis of the structure of random number generators) and practical ones (e.g., empirical experimentation, software implementation) are covered.