Markov Chains, Queueing, Martingales :
The Poisson process, the compound Poisson process, discrete time Markov chains: classification of states, stationary distributions, time reversibility. Continuous time Markov chains. Markov queueing systems (M/M/c/K), Markovian queueing systems (M/Er/1, Er/M/1), Markov networks, M/G/1 queueing systems, Pollaczek-Khinchin transform equation. Discrete time martingales: Conditional expectation, martingale convergence theorems, Doob’s inequality, optional stopping Theorems. Birkhoff’s ergodic theorem.
Time Series :
Basic forecasting Tools (Time pots and time series patterns, Seasonal plots, Scatter plots, Auto correlation, Prediction intervals, Least Square estimation), Time series models (Auto regressive (AR) models, Moving Average models (MA), Auto Regressive Moving Average (ARMA), Auto Regressive Integrated Moving Average (ARIMA), Exponential Smoothing), Box-Jenkins methodology for ARIMA models, Assumptions in Box-Jenkins fitting models, Forecasting using ARIMA models, Introduction to Non –Linear time series model.