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...)