Controlled Stochastic Processes

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Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

Explores dynamic programming for optimizing decision-making processes over time, using real-world examples like oil extraction and stock trading.

Explores accelerating the Value Iteration algorithm using control theory and matrix splitting techniques to achieve faster convergence.

Explores Bourgain's theorem on sparsest cut in graphs, emphasizing semimetrics and cut optimization.

Explores Infinite-Horizon Linear Quadratic (LQ) optimal control, emphasizing solution methods and practical examples.

Explores the benefits of deeper networks in deep learning and the importance of over-parameterization and generalization.

Covers weak solutions in the finite element method, emphasizing continuity and the Cauchy-Schwarz inequality.

Explores Nonlinear Model Predictive Control, covering stability, optimality, pitfalls, and examples.

Explores Markov chains, transition matrices, distribution, and random walks.

Explores asset selling dynamics, optimal revenue policy, acceptance thresholds, and commodity price impact.