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Mathematics
Stochastic Processes (Web)
Syllabus
Co-ordinated by :
IIT Guwahati
Available from :
2016-09-07
Lec :
1
Modules / Lectures
Probability Essentials
Introduction
Random Variables and Probability Distributions
Random Vectors and Expectations
Sequences of Random Variables
References and Exercises 1
Introduction to Stochastic Processes
What are Stochastic Processes?
Classes of Stochastic Processes
References and Exercises 2
Discrete-Time Markov Chains
Introduction and Examples
Classification of States – I
Classification of States – II
Stability of Markov Chains
Reducible Markov Chains
Reversed and Time-Reversible Markov Chains
References and Exercises 3
Continuous-Time Markov Chains
Definition and Kolmogorov Equations
Limiting and Stationary Distributions
Poisson Processes – I
Poisson Processes – II
Birth-Death Processes
M/M/1 Queueing Model
Simple Markovian Queueing Models
References and Exercises 4
Martingales
Filtrations and Conditional Expectations
Conditional Expectations
Generated ?-fields
Martingales, Sub-martingales and Super-martingales
Stopping Times and Inequalities
Convergence Theorems
References and Exercises 5
Brownian Motion
Brownian Motion
Properties of Brownian Motion – I
Properties of Brownian Motion – II
Processes derived from Brownian Motion
Stochastic Differential Equations and Itô Integrals
Itô’s Formula
SDEs and their Applications in Finance
References and Exercises 6
Renewal Processes
Renewal Function and Renewal Equation
Generalized Renewal Processes and Renewal Limit Theorems
Markov Renewal and Markov Regenerative Processes
Non-Markovian Queues
Non-Markovian Queues (contd.) 1
Non-Markovian Queues (contd.) 2
References and Exercises 7
Branching Processes
Galton-Watson Process
Properties of GW Process
Markov Branching Process
References and Exercises 8
Stationary Processes
Stationary Processes
Some Special Stationary Processes
References and Exercises 9
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