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Topics for Stochastic modeling:
Dynamics of stochastic systems , assessment quality of service systems, management , control of inventory, renewal and replacement strategies, examples of discrete time Markov chains, Chapman-Kolmogorov equations, Classification of States, Long run behavior of Markov chains.
Absorption probabilities , expected times to absorption, Statistical aspects of Markov chains, The mover-stayer model, Application of a Markov chain , mover-stayer model to modeling, repayment behavior of bank loans’ grantees, Poisson process.
The Kolmogorov differential equations, Limiting behavior of continuous time Markov chains, Birth and death processes, Statistical aspects , continuous time Markov chains, Conditional expectation, Definition of a martingale and examples.
Optional stopping theorem, Applications to random walks, Martingales in option pricing , Motivation, properties of Brownian motion, Geometric Brownian motion, Continuous time martingales.
Optional stopping theorem, Using martingales to analyze Brownian motion, Diffusions as generalizations of Brownian motion
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