Roll Number
11i190009
Category
TA
Topics for PhD Qualifiers
Optimization Techniques
Stochastic Process
Stochastic Process
Elective1
Probability Theory
Syllabus:
- Construction of Probability Measure.
- Conditional Probability and Independence.
- Random Variables on a countable Space.
- Integration with respect to a Probability Measure.
- Independent Random variables.
- Probability Distributions on R.
- Sum of independent random variables.
- Convergence of random variables.
- Conditional expectation
- Martingales
- Super and sub Martingales.
- Martingale Inequalities.
- Martingale Convergence Theorems.
Reference books:
Probability Essentials by Jean Jacod, Philip Protter.
Probability and Measure by Patrick Billingsley.
Syllabus:
- Construction of Probability Measure.
- Conditional Probability and Independence.
- Random Variables on a countable Space.
- Integration with respect to a Probability Measure.
- Independent Random variables.
- Probability Distributions on R.
- Sum of independent random variables.
- Convergence of random variables.
- Conditional expectation
- Martingales
- Super and sub Martingales.
- Martingale Inequalities.
- Martingale Convergence Theorems.
Reference books:
Probability Essentials by Jean Jacod, Philip Protter.
Probability and Measure by Patrick Billingsley.
Elective2
Simulation
Syllabus:
Concepts in discrete event system simulation; approaches based on event scheduling, process interaction and activity scanning. Examples of systems such as job shop scheduling & extensions, queuing systems, inventory systems. Use of linked lists in implementing some common data structures encountered in simulation. Simulation in C. Concepts of object oriented simulation. Simulation packages.
Overview of basic concepts from probability and statistics concerning random variables, correlation, estimation, confidence intervals, hypothesis testing. Generation and testing of random numbers. Generation of random variates, random vectors, correlated random variates and stochastic processes. Input modeling; useful probability distributions; hypothesizing families of distributions, estimation of parameters, testing goodness of fit. Simulation Output data analysis for a single system; statistical analyses for transient systems and systems in statistical equilibrium.
Syllabus:
Concepts in discrete event system simulation; approaches based on event scheduling, process interaction and activity scanning. Examples of systems such as job shop scheduling & extensions, queuing systems, inventory systems. Use of linked lists in implementing some common data structures encountered in simulation. Simulation in C. Concepts of object oriented simulation. Simulation packages.
Overview of basic concepts from probability and statistics concerning random variables, correlation, estimation, confidence intervals, hypothesis testing. Generation and testing of random numbers. Generation of random variates, random vectors, correlated random variates and stochastic processes. Input modeling; useful probability distributions; hypothesizing families of distributions, estimation of parameters, testing goodness of fit. Simulation Output data analysis for a single system; statistical analyses for transient systems and systems in statistical equilibrium.
PhD. Supervisor (if decided)
Prof. Veeraruna Kavitha
Proposed Research Plan (if decided)
Working on performance measure of Heterogeneous Network in random environment, interaction of mobile user's doing brownian motion with same system.