Fundamental tools for stochastic simulation

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My research program concerns the development and study of fundamental tools (mathematical, statistical, and computational) for modeling, simulating, and optimizing systems that involve uncertainty. The demand for improved simulation tools has increased tremendously in recent years. Stochastic (Monte Carlo) simulation is used heavily 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. Stochastic simulation and optimization have been key ingredients in the spectacular recent progress in machine learning, for example. ******My goal in this context is to contribute new ideas and methods to the Monte Carlo tool set, and improve our understanding of the existing ones. I contribute to theoretical aspects (such as convergence analysis of simulation algorithms and mathematical analysis of the structure of random number generators) and practical ones (e.g., empirical experimentation, software implementation, and adaptation to specific real-life applications). My main focus in on general tools that have a wide range of applications, such as random number and random variate generators, quasi-Monte Carlo methods, variance-reduction methods, rare-event simulation techniques, and stochastic optimization methods. I also work on selected applications, e.g., in finance, reliability, and management of 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 for simulation on various types of platforms, in particular for massively-parallel computers, and methods to test such generators; (2) develop and study randomized quasi-Monte Carlo (RQMC) methods, which replace the independent vectors of random numbers used in Monte Carlo (MC) simulations by points that cover the space more uniformly than random points, to improve accuracy, and provide effective practical tools that implement these methods; (3) design and study efficient rare-event simulation methods, for settings in which certain events that occur very rarely have a large impact on the performance measure of interest, and study applications of these; (4) develop simulation-based optimization methods for decision making in complex stochastic systems; (5) develop effective methods to build stochastic models of complex service systems that involve humans, based on large amounts of data, to support decision making (e.g., emergency services, call centers, healthcare systems, finance, network economics for the Internet, reliability problems, etc.).**