NOC:Stochastic Processes

Lecture 1 - Introduction and motivation for studying stochastic processes

Lecture 2 - Probability space and conditional probability

Lecture 3 - Random variable and cumulative distributive function

Lecture 4 - Discrete Uniform Distribution, Binomial Distribution, Geometric Distribution, Continuous Uniform Distribution, Exponential Distribution, Normal Distribution and Poisson Distribution

Lecture 5 - Joint Distribution of Random Variables

Lecture 6 - Independent Random Variables, Covariance and Correlation Coefficient and Conditional Distribution

Lecture 7 - Conditional Expectation and Covariance Matrix

Lecture 8 - Generating Functions, Law of Large Numbers and Central Limit Theorem

Lecture 9 - Problems in Random variables and Distributions

Lecture 10 - Problems in Random variables and Distributions (Continued...)

Lecture 11 - Problems in Random variables and Distributions (Continued...)

Lecture 12 - Problems in Random variables and Distributions (Continued...)

Lecture 13 - Problems in Sequences of Random Variables

Lecture 14 - Problems in Sequences of Random Variables (Continued...)

Lecture 15 - Problems in Sequences of Random Variables (Continued...)

Lecture 16 - Problems in Sequences of Random Variables (Continued...)

Lecture 17 - Definition of Stochastic Processes, Parameter and State Spaces

Lecture 18 - Classification of Stochastic Processes

Lecture 19 - Examples of Discrete Time Markov Chain

Lecture 20 - Examples of Discrete Time Markov Chain (Continued...)

Lecture 21 - Bernoulli Process

Lecture 22 - Poisson Process

Lecture 23 - Poisson Process (Continued...)

Lecture 24 - Simple Random Walk and Population Processes

Lecture 25 - Introduction to Discrete time Markov Chain

Lecture 26 - Introduction to Discrete time Markov Chain (Continued...)

Lecture 27 - Examples of Discrete time Markov Chain

Lecture 28 - Examples of Discrete time Markov Chain (Continued...)

Lecture 29 - Introduction to Chapman-Kolmogorov equations

Lecture 30 - State Transition Diagram and Examples

Lecture 31 - Examples

Lecture 32 - Introduction to Classification of States and Periodicity

Lecture 33 - Closed set of States and Irreducible Markov Chain

Lecture 34 - First Passage time and Mean Recurrence Time

Lecture 35 - Recurrent State and Transient State

Lecture 36 - Introduction and example of Classification of states

Lecture 37 - Example of Classification of states (Continued...)

Lecture 38 - Example of Classification of states (Continued...)

Lecture 39 - Example of Classification of states (Continued...)

Lecture 40 - Introduction and Limiting Distribution

Lecture 41 - Example of Limiting Distribution and Ergodicity

Lecture 42 - Stationary Distribution and Examples

Lecture 43 - Examples of Stationary Distributions

Lecture 44 - Time Reversible Markov Chain and Examples

Lecture 45 - Definition of Reducible Markov Chains and Types of Reducible Markov Chains

Lecture 46 - Stationary Distributions and Types of Reducible Markov chains

Lecture 47 - Type of Reducible Markov Chains (Continued...)

Lecture 48 - Gambler's Ruin Problem

Lecture 49 - Introduction to Continuous time Markov Chain

Lecture 50 - Waiting time Distribution

Lecture 51 - Chapman-Kolmogorov Equation

Lecture 52 - Infinitesimal Generator Matrix

Lecture 53 - Introduction and Example Of Continuous time Markov Chain

Lecture 54 - Limiting and Stationary Distributions

Lecture 55 - Time reversible CTMC and Birth Death Process

Lecture 56 - Steady State Distributions, Pure Birth Process and Pure Death Process

Lecture 57 - Introduction to Poisson Process

Lecture 58 - Definition of Poisson Process

Lecture 59 - Superposition and Deposition of Poisson Process

Lecture 60 - Compound Poisson Process and Examples

Lecture 61 - Introduction to Queueing Systems and Kendall Notations

Lecture 62 - M/M/1 Queueing Model

Lecture 63 - Little's Law, Distribution of Waiting Time and Response Time

Lecture 64 - Burke's Theorem and Simulation of M/M/1 queueing Model

Lecture 65 - M/M/c Queueing Model

Lecture 66 - M/M/1/N Queueing Model

Lecture 67 - M/M/c/K Model, M/M/c/c Loss System, M/M/? Self Service System

Lecture 68 - Transient Solution of Finite Birth Death Process and Finite Source Markovian Queueing Model

Lecture 69 - Queueing Networks Characteristics and Types of Queueing Networks

Lecture 70 - Tandem Queueing Networks

Lecture 71 - Stationary Distribution and Open Queueing Network

Lecture 72 - Jackson's Theorem, Closed Queueing Networks, Gordon and Newell Results

Lecture 73 - Wireless Handoff Performance Model and System Description

Lecture 74 - Description of 3G Cellular Networks and Queueing Model

Lecture 75 - Simulation of Queueing Systems

Lecture 76 - Definition and Basic Components of Petri Net and Reachability Analysis

Lecture 77 - Arc Extensions in Petri Net, Stochastic Petri Nets and examples

Lecture 78 - Generalized Stochastic Petri Net

Lecture 79 - Generalized Stochastic Petri Net (Continued...)

Lecture 80 - Conditional Expectation and Examples

Lecture 81 - Filtration in Discrete time

Lecture 82 - Remarks of Conditional Expectation and Adaptabilty

Lecture 83 - Definition and Examples of Martingale

Lecture 84 - Examples of Martingale (Continued...)

Lecture 85 - Examples of Martingale (Continued...)

Lecture 86 - Doob's Martingale Process, Sub martingale and Super Martingale

Lecture 87 - Definition of Brownian Motion

Lecture 88 - Definition of Brownian Motion (Continued...)

Lecture 89 - Properties of Brownian Motion

Lecture 90 - Processes Derived from Brownian Motion

Lecture 91 - Processes Derived from Brownian Motion (Continued...)

Lecture 92 - Processes Derived from Brownian Motion (Continued...)

Lecture 93 - Stochastic Differential Equations

Lecture 94 - Stochastic Differential Equations (Continued...)

Lecture 95 - Stochastic Differential Equations (Continued...)

Lecture 96 - Ito Integrals

Lecture 97 - Ito Integrals (Continued...)

Lecture 98 - Ito Integrals (Continued...)

Lecture 99 - Renewal Function and Renewal Equation

Lecture 100 - Renewal Function and Renewal Equation (Continued...)

Lecture 101 - Renewal Function and Renewal Equation (Continued...)

Lecture 102 - Generalized Renewal Processes and Renewal Limit Theorems

Lecture 103 - Generalized Renewal Processes and Renewal Limit Theorems (Continued...)

Lecture 104 - Generalized Renewal Processes and Renewal Limit Theorems (Continued...)

Lecture 105 - Markov Renewal and Markov Regenerative Processes

Lecture 106 - Markov Renewal and Markov Regenerative Processes (Continued...)

Lecture 107 - Markov Renewal and Markov Regenerative Processes (Continued...)

Lecture 108 - Markov Renewal and Markov Regenerative Processes (Continued...)

Lecture 109 - Non Markovian Queues

Lecture 110 - Non Markovian Queues (Continued...)

Lecture 111 - Non Markovian Queues (Continued...)

Lecture 112 - Stationary Processes

Lecture 113 - Stationary Processes (Continued...)

Lecture 114 - Stationary Processes (Continued...)

Lecture 115 - Stationary Processes (Continued...) and Ergodicity

Lecture 116 - G1/M/1 queue

Lecture 117 - G1/M/1 queue (Continued...)

Lecture 118 - G1/M/1/N queue and examples

Lecture 119 - Galton-Watson Process

Lecture 120 - Examples and Theorems

Lecture 121 - Theorems and Examples (Continued...)

Lecture 122 - Markov Branching Process

Lecture 123 - Markov Branching Process Theorems and Properties

Lecture 124 - Markov Branching Process Theorems and Properties (Continued...)