Course Details Probability: Probability models and axioms, conditioning and Bayes' rule, independence discrete random variables; probability mass functions; expectations, examples, multiple discrete random variables: joint PMFs, expectations, conditioning, independence, continuous random variables, probability density functions, expectations, examples, multiple continuous random variables, continuous Bayes rule, derived distributions; convolution; covariance and correlation, iterated expectations, sum of a random number of random variables. Stochastic process: Bernoulli process, Poisson process, Markov chains. Weak law of large umbers, central limit theorem. Statistics: Bayesian statistical inference, point estimators, parameter estimators, test of hypotheses, tests of significance. . Course References: TEXT: D. Bertsekas and J. Tsitsiklis, Introduction to Probability, 2nd ed, Athena Scientific, 2008.
Department of Mathematics
Indian Institute Of Technology Madras , Chennai
Professor
CURRENT RESEARCH INTERESTNonlinear Analysis - Variational Inequalities, Optimization and Non-smooth Analysis
CONTACT044 - 2257 4619/4601
vetri
RESEARCH GROUPS PERSONAL HOME PAGE https://home.iitm.ac.in/vetriTeaching :
Recent Publications :
Finite Convergence and Sharp Minima for Quasi-Equilibrium Problems
Authors : K Mittal, P Gautam and V Vetrivel
Journal : Journal of Optimization Theory and Applications
Year: 2024
Parameterized Douglas-Rachford dynamical system for monotone inclusion problems
Authors : V. Vetrivel, P. Gautam, K. Som
Journal : Applied set-valued analysis and optimization
Volume :5 (1) Page: 19-29
Year: 2023
Pointwise well-posedness of a set-valued optimization problem at a weak solution
Authors : V Vetrivel and K Som
Journal : The Journal of Analysis
Volume :31 Page: 187–199
Year: 2023
Well-posedness for the split equilibrium problem
Authors : S Dey, V Vetrivel and HK Xu
Journal : Optimization Letters
Volume :18 Page: 977-989
Year: 2023
Global well-posedness of set-valued optimization with application to uncertain problems
Authors : V Vetrivel and K Som
Journal : Journal of Global Optimization
Volume :88 (8) Page: 511-539
Year: 2022
A note on pointwise well-posedness of set-valued optimization problems
Authors : V Vetrivel and K Som
Journal : Journal of Optimization Theory and Applications
Volume :192 Page: 628-647
Year: 2022
On robustness for set-valued optimization problems
Authors : V Vetrivel and K Som
Journal : Journal of Global Optimization
Volume :79 Page: 905–925
Year: 2021
Notes on the neural network approach to inverse variational inequalities
Authors : V Vetrivel and Hong-Kun Xu, Soumitra Dey
Journal : Optimization
Volume :70 Page: 5-6, 901-910
Year: 2021
A neural network method for monotone variational inclusions
Authors : V Vetrivel and Hong-Kun Xu, Soumitra Dey
Journal : Nonlinear and Convex Anal
Volume :20 Page: 11, 2387-2395
Year: 2019
On Approximate solution to Inverse Quasi-Variational Inequality Problem
Authors : V Vetrivel and S Dey
Journal : Sci. Math. Japonica
Volume :81 Page: 301-306
Year: 2018
On Nonexistence of bent – negabent rotation symmetric Boolean functions
Authors : V. Vetrivel, B. Mandal, B. Singh, S. Gangopadhyay, and S. Maitra
Journal : Discrete Appl. Math
Volume :236 Page: 1-6
Year: 2018