Roll Number
13i190010
Category
TA
Topics for PhD Qualifiers
Compulsory Subject: (i) Optimisation Techniques, (ii) Stochastic Models
Elective1
Stochastic : Galton-Watson Process, Multitype Discrete time Branching
Process,
Simple continuous-time Markovian Branching Process, Multitype continuous
time Markovian Branching Process,
Extinction probability, Martingale representation,
Brownian motion, Introduction to Ito calculus.
Process,
Simple continuous-time Markovian Branching Process, Multitype continuous
time Markovian Branching Process,
Extinction probability, Martingale representation,
Brownian motion, Introduction to Ito calculus.
Elective2
Probability theory:- Continuous time Markov process, Renewal theory,
Probability space, Sigma-algebra, Measurable functions, Integration/Expectation,
Conditional expectation, Modes of convergence for sequences of random variables:
almost sure convergence, convergence in probability, Convergence in Lp space, weak
convergence.
Discrete time Martingales, Basics of Continuous-time Martingales
Probability space, Sigma-algebra, Measurable functions, Integration/Expectation,
Conditional expectation, Modes of convergence for sequences of random variables:
almost sure convergence, convergence in probability, Convergence in Lp space, weak
convergence.
Discrete time Martingales, Basics of Continuous-time Martingales
PhD. Supervisor (if decided)
Prof. Veeraruna Kavitha