Course Name: 

Stochastic Processes (IT443)


B.Tech (AI)


Programme Specific Electives (PSE)

Credits (L-T-P): 

(3-0-2) 4


Discrete-time Markov chains: Definition and examples of discrete-time Markov chains, Chapman-Kolmogorov equations, Long run behaviour of Markov chains, Absorption probabilities and expected times to absorption, Statistical aspects of Markov chains, The mover-stayer model, Application of a Markov chain and mover-stayer model to modelling.Continuous-time Markov chains: Definition of a continuous-time Markov chain and examples, Poisson process, The Kolmogorov differential equations, Limiting behaviour of continuous-time Markov chains, birth and death processes, Statistical aspects and applications of continuous-time Markov chains. Discrete-time martingales: Conditional expectation, Definition of a martingale and examples, Optional stopping theorem, Applications to random walks, Martingales in option pricing- a simple example; Brownian Motion and its generalizations: Motivation, definition and properties of Brownian motion, Geometric Brownian motion, Continuous-time martingales, Optional stopping theorem;Stochastic calculus: Stochastic integration, Ito’s formula, Black-Scholes option pricing formula


Introduction to Probability and Stochastic Processes with Applications, Castaneda, Arunachalam, Dharmaraja, Wiley, 2012
G.F. Lawler, Introduction to Stochastic Processes (Second Edition), Chapman and Hall, Probability Series, 2006.
An Introduction to Stochastic Modeling, H.M. Taylor and S. Karlin, Academic Press, Third Edition


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