This course explanations and expositions of stochastic processes concepts which they need for their experiments and research. It also covers theoretical concepts pertaining to handling various stochastic modeling. This course provides classification and properties of stochastic processes, stationary processes, discrete and continuous time Markov chains and simple Markovian queueing models.

Week

Topics

1

Probability theory refresher

1. Introduction to stochastic process

2. Introduction to stochastic process (contd.)

2

Probability theory refresher (contd.)

1. Problems in random variables and distributions

2. Problems in Sequence of random variables

3. Definition, classification and Examples

3

Definition and simple stochastic process

1. Simple stochastic processes

Stationary and Auto Regressive Processes

1. Stationary processes

2. Autoregressive processes

4

Discrete-time Markov chains

1. Introduction, Definition and Transition Probability Matrix

2. Chapman-Kolmogorov Equations

5

Discrete-time Markov chains (contd.)

1. Classification of States and Limiting Distributions

2. Limiting and Stationary Distributions

3. Limiting Distributions, Ergodicity and stationary distributions

6

Discrete-time Markov chains (contd.)

1. Time Reversible Markov Chain, Application of Irreducible Markov chains in

Queueing Models2. Reducible Markov Chains

7

Continuous-time Markov chains

1. Definition, Kolmogrov Differential Equation and Infinitesimal Generator Matrix

2. Limiting and Stationary Distributions, Birth Death Processes

3. Poisson processes

8

Continuous-time Markov Chains (contd.)

1. M/M/1 Queueing model

2. Simple Markovian Queueing Models

A basic course on Probability 1. J Medhi, Stochastic Processes, 3 rd edition, New Age International Publishers, 2009 2. Liliana Blanco Castaneda, Viswanathan Arunachalam, Selvamuthu Dharmaraja, Introduction to Probability and Stochastic Processes with Applications, Wiley, 2012. 3. Kishor S. Trivedi, Probability and Statistics with Reliability, Queuing, and Computer Science Applications, 2nd Edition, Wiley, 2002.

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