Learn · Applied Stochastic Processes
Lecture 34 of 60Week 7
Lecture 34 : CTMCs via a sequence of DTMCs
Prof. Swanand Ravindra Khare Prof. Amitalok Jayant Budkuley · IIT Kharagpur
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All the lectures
- Lecture 01 : Introduction to Probability
- Lecture 02 : Conditional Probability
- Lecture 03 : Total Probability and Bayes’ Rule
- Lecture 04 : Random Variables (Discrete)
- Lecture 05 : Discrete Random Variables & Special Distributions
- Lecture 6 : Continuous Random Variables
- Lecture 7 : Expectation, Variance and Joint Distributions
- Lecture 8 : Conditional pmfs and pdfs, Independence
- Lecture 9 : Conditional Expectation and Conditional Variance
- Lecture 10 : Functions of random variable, sampling, limit theorems
- Lecture 11 : Introduction to Stochastic Processes, Hitting Time
- Lecture 12 : Markov Chains
- Lecture 13 : Chapman–Kolmogorov Equations
- Lecture 14 : Classification of States
- Lecture 15 : Limiting and Stationary Distributions
- Lecture 16 : Existence and Uniqueness of Stationary Distributions
- Lecture 17 : Positive and Null Recurrence
- Lecture 18 : Computation of Stationary Distribution and Gambler's Ruin
- Lecture 19 : Mean Time in Transient States and Branching Processes
- Lecture 20 : Hidden Markov Models
- Lecture 21 : Introduction to counting processes and Bernoulli random processes
- Lecture 22 : Foundations of discrete-time Bernoulli random processes
- Lecture 23 : Bernoulli random processes: Alternate synthesis approaches
- Lecture 24 : Counting function of Bernoulli random processes
- Lecture 25 : Operations on Bernoulli random processes, and summary
- Lecture 26 : Foundations of continuous-time Poisson random processes
- Lecture 27 : Poisson counting processes: Dynamical system approach, counting function
- Lecture 28 : Bernoulli approximation of Poisson processes, Key properties and illustrations via counting functions of Poisson counting processes
- Lecture 29 : Operations on Poisson counting processes, Illustrative examples
- Lecture 30 : Illustrative examples involving Poisson counting processes, summary, and comparison of Bernoulli and Poisson counting processes.
- Lecture 31 : Continuous-time Markov Chains (CTMCs): Introduction
- Lecture 32 : CTMCs Foundations 1: Formal definitions of important quantities associated with CTMCs
- Lecture 33 : CTMCs Foundations 2: Transition rates, Generator, Embedded chains
- Lecture 34 : CTMCs via a sequence of DTMCs
- Lecture 35 : Birth-Death CTMCs: Foundations
- Lecture 36 : Birth-Death CTMCs: Illustrations
- Lecture 37 : CTMCs: A re-look using first principles approach (I)
- Lecture 38 : CTMCs: A re-look using first principles approach (II)
- Lecture 39 : Transient analysis of CTMCs
- Lecture 40 : Steady state analysis of CTMCs, Reversibility, birth-death chains and reversibility
- Lecture 41 : Renewal process: Foundations, examples, applications
- Lecture 42 : Counting function of Renewal processes
- Lecture 43 : Renewal function and Elementary renewal theorem
- Lecture 44 : CLT for Renewal processes, Renewal reward theorem, Illustration via age of renewal
- Lecture 45 : Renewal process: Illustrations and extensions
- Lecture 46 : Queuing theory: Foundations, applications, Illustrative example via timing diagram
- Lecture 47 : Discrete-time Queues: Geo/Geo/1 queues
- Lecture 48 : Continuous-time Queues: M/M/* queues
- Lecture 49 : Delay models and delay analysis in Queueing theory
- Lecture 50 : Queueing Theory: General queues, Burke's theorem, Tandem queues, examples
- Lecture 51 : Introduction to Brownian Motion and Random Walks
- Lecture 52 : Properties and Joint Distributions of Brownian Motion
- Lecture 53 : White Noise and Stochastic Integrals
- Lecture 54 : Gaussian Processes and Brownian Bridge
- Lecture 55 : Stationary Processes and Random Telegraph Signal
- Lecture 56 : Second-Order Stationarity and Auto-Regressive Processes
- Lecture 57 : Linear Systems and Spectral Density
- Lecture 58 : Pricing Stock Options & Arbitrage Theorem
- Lecture 59 : Martingales and Geometric Brownian Motion
- Lecture 60 : Black-Scholes Formula & Jump Processes