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.

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