M.Tech I Year II Semester (R19)
To introduce Probability Review and Introduction to Stochastic Processes (SPs) To introduce the concept of Stationary Processes To introduce the Concepts of DTMCs and CTMCs Study about Brownian Motion and Martingales Study of Renewal Processes and Branching Processes
Probability Theory Refresher: Axiomatic construction of probability spaces, random variables and vectors, probability distributions, functions of random variables; mathematical expectations, transforms and generating functions, laws of large numbers, central limit theorem. Introduction to Stochastic Processes (SPs): Definition and examples of SPs, classification of random processes according to state space and parameter space, types of SPs
Stationary Processes: Weakly stationary and strongly stationary processes, moving average and auto regressive processes. Discrete-time Markov Chains (DTMCs): Definition and examples of MCs, transition probability matrix, Chapman-Kolmogorov equations; calculation of n-step transition probabilities, Random walk and gambler’s ruin problem, applications.
Continuous-time Markov Chains (CTMCs): Kolmogorov- Feller differential equations, infinitesimal generator, Poisson process, birth-death process, stochastic Petri net Martingales: Conditional expectations, definition and examples of martingales.
Brownian Motion: Wiener process as a limit of random walk; process derived from Brownian motion, stochastic differential equation, stochastic integral equation, Ito formula, Some important SDEs and their solutions, applications to finance.
Renewal Processes: Renewal function and its properties, renewal theorems, cost/rewards associated with renewals, Markov renewal and regenerative processes, non Markovian queues, applications of Markov regenerative processes. Branching Processes: Definition and examples branching processes, probability generating function, mean and variance, Galton-Watson branching process, probability of extinction.
J. Medhi, Stochastic Processes, 3rd Edition, New Age International, 2009. S.M. Ross, Stochastic Processes, 2nd Edition, Wiley, 1996. S Karlin and H M Taylor,A First Course in Stochastic Processes, 2nd Edition, Academic Press, 1975
“Modeling and Analysis of Stochastic Systems", V. G. Kulkarni, CRC, 2nd Edition, 2010 “Introduction to Probability Models”, Sheldon Ross, AP, 9th Ed., 2007. “Stochastic Modeling and the Theory of Queues”, Ronald Wolff, Prentice Hall, 1989. M.Tech. (Data Science) I Year II Semester
Loading Question Papers
Fetching data from database...