Math. 631 Multivariate Analysis
The multivariate normal distribution – Classification of observation – Bayesian estimation – Linear statistical methods.
Math. 632 Probability Theory
Part (1): Some complementary topics concerning the theory of probability using measure theory – Part (2): Limit theorems for sums of independent random variables.
Math. 633 Stochastic Processes
Markov Chain: stationary M.C. and non-stationary M.C - Inventory Problems - Transient behavior - Stationary distribution - Problem of emptiness - Queues: some variants of the queuing systems, tandem queues.
Math. 634 Order Statistics
Basic distribution theory – Expected values and moments – Bounds and approximations for moments of order statistics – Order statistics in estimation and hypothesis testing.
Math. 635 Theory of Martingales
Martingales – Stopping times – Stopped martingales – Adjustment of two martingales – Sub martingales – Stopped sub martingales – Adjustment of two sub martingales – Regular martingales – Uniform integrability – Doob’s maximal inequality – Optional sampling theorem – Reversed martingales – Supper martingales – Krickeberg’s decomposition theorem – Doob’s and Rise decompositions – Young functions – Orlicz spaces – Properties and generalized Doob’s maximal inequalities in LΦ space.