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, discrete and
continuous time Markov chains, simple Markovian queueing models,
applications of CTMC, martingales, Brownian motion, renewal
processes, branching processes, stationary and autoregressive
processes.
Week
Topics
1.
Probability theory
refresher
Introduction to stochastic process
Introduction to stochastic process (contd.)
2.
Probability theory refresher (contd.) Problems in random variables and distributions
Problems in Sequence of random variables
3.
Definition and simple
stochastic process
Definition, classification and Examples
Simple stochastic processes
4.
Discrete-time Markov
chains
Introduction, Definition and Transition Probability Matrix
Chapman-Kolmogorov Equations
Classification of States and Limiting Distributions
5.
Discrete-time Markov
chains (contd.)
Limiting and Stationary Distributions
Limiting Distributions, Ergodicity and stationary
distributions
Time Reversible Markov Chain, Application of Irreducible
Markov chains in Queueing Models
Reducible Markov Chains
6.
Continuous-time Markov
chains
Definition, Kolmogrov Differential Equation and
Infinitesimal Generator Matrix
Limiting and Stationary Distributions, Birth Death Processes
Poisson processes
Applications of CTMC Queueing networks
Communication systems
Stochastic Petri Nets
9.
Martingales
Conditional Expectation and filteration
Definition and simple examples
10.
Brownian Motion Definition and Properties
Processes Derived from Brownian Motion
11.
Renewal Processes
Renewal Function and Equation
Generalized Renewal Processes and Renewal Limit Theorems
Markov Renewal and Markov Regenerative Processes
Non Markovian Queues
Application of Markov Regenerative Processes
12.
Branching Processes, Stationary and Autoregressive
Processes
A basic course on Probability
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