Stochastic Processes video lectures, S. Dharmaraja of IIT Delhi

Home »Mathematics »IIT Delhi » Stochastic Processes

Stochastic Processes

Lecture 1: Mod-01 Lec-01 Introduction to Stochastic Processes

Download:   MP4, FLV and 3GP 15298 views

SEE: Guide to Download NPTEL Video Lecture

Lecture Details :

Stochastic Processes by Dr. S. Dharmaraja, Department of Mathematics, IIT Delhi. For more details on NPTEL visit

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 :

Syllabus | Handouts | Citation |

Above free video lectures are presented by IIT Delhi, under NPTEL program, there are still 6000+ iit video lectures are available.

Other Mathematics Courses

» check out the complete list of Mathematics Video lectures          


Get Your Degree!

Find schools and get information on the program that’s right for you.

Powered by Campus Explorer


Post your Comments