Stochastic Simulation and Monte Carlo Methods

Modeling and simulation of stochastic systems for uncertainty quantification and decision making. Topics include generation of univariate and multivariate random variables (inversion, acceptance-rejection, Gaussian models, copulas), simulation of Brownian motion and stochastic differential equations, statistical output analysis (confidence intervals and stopping rules), variance reduction (control variates, stratification, conditional Monte Carlo), bias analysis and removal, randomized multilevel Monte Carlo, and steady-state estimation via regenerative methods. Emphasis is placed on modular simulation architectures that integrate modeling, sampling, variance reduction, debiasing, and statistical certification. Applications arise in engineering, finance, operations research, and machine learning. Prerequisites: Calculus-based probability and basic statistics. Students are expected to implement and validate simulation algorithms using modern computational tools.