Lecture Details :
Stochastic Processes by Dr. S. Dharmaraja, Department of Mathematics, IIT Delhi. For more details on NPTEL visit http://nptel.iitm.ac.in
Course Description :
Probability Theory Refresher: Axiomatic construction of probability spaces, random variables and vectors, probability distributions, functions of random variables; mathematical expectations, transforms and generating functions, modes of convergence of sequences of random variables, 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, elementary problems.
Discrete-time Markov Chains (MCs): Definition and examples of MCs, transition probability matrix, Chapman-Kolmogorov equations; calculation of n-step transition probabilities, limiting probabilities, classification of states, ergodicity, stationary distribution, transient MC; random walk and gamblerís ruin problem, applications.
Continuous-time Markov Chains (MCs): Kolmogorov- Feller differential equations, infinitesimal generator, Poisson process, birth-death process, Applications to queueing theory, inventory analysis, communication networks, finance and biology.
Brownian Motion: Wiener process as a limit of random walk; first -passage time and other problems, applications to finance.
Branching Processes: Definition and examples branching processes, probability generating function, mean and variance, Galton-Watson branching process, probability of extinction.
Renewal Processes: Renewal function and its properties, elementary and key renewal theorems, cost/rewards associated with renewals, Markov renewal and regenerative processes, applications.
Stationary Processes: Weakly stationary and strongly stationary processes, moving average and auto regressive processes.
Martingales: Conditional expectations, definition and examples of martingales, inequality, convergence and smoothing properties, applications in finance.
Other Resources :
Other Mathematics Courses
- Introduction to Probability and Statistics,Fall 2011 by UC Berkeley
- Linear Algebra - Khan Academy by Khan Academy
- Probability by Khan Academy
- Statistics PL04 - Introduction to Probability by Other
- Math 3C: Probability for Math Science by UCLA
- AMC Sequences and Series by Other
- Math 60 - Introductory Algebra-1st Term by Portland Community College
- Discrete Structures by IIT Madras
- AMC Function by Other
- Mobius Function by Other
» check out the complete list of Mathematics Video lectures