AI301

Course Name: 

Stochastic Processes (AI301)

Programme: 

B.Tech (AI)

Category: 

Programme Core (PC)

Credits (L-T-P): 

(4-0-0) 4

Content: 

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

References: 

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

Department: 

Information Technology
 

Contact us

Head of the Department,
Department of Information Technology,
National Institute of Technology Karnataka,
SurathkalP. O. Srinivasnagar, Mangalore - 575 025
Ph.:    +91-824-2474056
Email:  hodit [at] nitk [dot] edu [dot] in
 

Web Admin: Sowmya Kamath S

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