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Topics For Applied Stochastic Processes:

Stochastic State Space Models

Models, Markov Chains, Gauss Markov Processes, Stochastic Context Free Grammars, Stochastic Simulation, Simulation based Stochastic Optimization, Recursive Least Squares to Discrete Optimization, Stochastic Approximation Algorithms and Analysis.

Bayesian Filtering

Optimal Filtering, Kalman and Hidden Markov Model Filters, Sequential Markov Chain Monte-Carlo, Continuous-time Stochastic Filtering Theory

Maximum Likelihood Estimation of Dynamical Systems

Asymptotic Properties of Maximum Likelihood Estimation, Expectation Maximization Algorithms, Hidden Markov Models, Gaussian State Space Models, Stochastic Context Free Grammars.

Markov Decision Processes

Finite horizon and infinite horizon problems, Structural Results using super modularity, Resource Allocation in Wireless Communications, Partially Observed Stochastic Control, Stochastic Sensor Scheduling.

Advanced Level Seminars

Stochastic Simulation of Biological Ion Channels at Atomic Scale, Primarily on Brownian dynamics simulations, Structural Results in Stochastic Games, Applications in Sensor Networks, Game Theory is a natural extension of Markov Decision Processes.

Random Signals

Intuitive Notion of Probability, Axiomatic Probability, Joint and Conditional Probability.

Independence

Random Variables, Probability Distribution and Density Functions

Expectation, Averages and Characteristic Function

Normal or Gaussian Random Variables, Impulsive Probability Density Functions, Multiple Random Variables

Correlation, Covariance, and Orthogonality

Sum of Independent Random Variables and Tendency toward Normal Distribution, Transformation of Random Variables.