Applied Stochastic Processes TSDX7D2Z5K

URI	`m2://res/TSDX7D2Z5K`
Kind	course
Creators	Amitalok Jayant Budkuley (instructor), Swanand Ravindra Khare (instructor)
Date	2026-01-17
MSC	60-XX
Scope	in
Ids	course 03w5sq511:111105901

Expressions

e1: edition

Language	en
Date	2026-01-17

m1: page, IIT Kharagpur (record). nptel 111105901
m2: page, 2026-01-17 (record). nptel 111105901

Contents

part 1: Week 1
session 1: Lecture 01 : Introduction to Probability
session 2: Lecture 02 : Conditional Probability
session 3: Lecture 03 : Total Probability and Bayes’ Rule
session 4: Lecture 04 : Random Variables (Discrete)
session 5: Lecture 05 : Discrete Random Variables & Special Distributions
part 2: Week 2
session 6: Lecture 6 : Continuous Random Variables
session 7: Lecture 7 : Expectation, Variance and Joint Distributions
session 8: Lecture 8 : Conditional pmfs and pdfs, Independence
session 9: Lecture 9 : Conditional Expectation and Conditional Variance
session 10: Lecture 10 : Functions of random variable, sampling, limit theorems
part 3: Week 3
session 11: Lecture 11 : Introduction to Stochastic Processes, Hitting Time
session 12: Lecture 12 : Markov Chains
session 13: Lecture 13 : Chapman–Kolmogorov Equations
session 14: Lecture 14 : Classification of States
session 15: Lecture 15 : Limiting and Stationary Distributions
part 4: Week 4
session 16: Lecture 16 : Existence and Uniqueness of Stationary Distributions
session 17: Lecture 17 : Positive and Null Recurrence
session 18: Lecture 18 : Computation of Stationary Distribution and Gambler's Ruin
session 19: Lecture 19 : Mean Time in Transient States and Branching Processes
session 20: Lecture 20 : Hidden Markov Models
part 5: Week 5
session 21: Lecture 21 : Introduction to counting processes and Bernoulli random processes
session 22: Lecture 22 : Foundations of discrete-time Bernoulli random processes
session 23: Lecture 23 : Bernoulli random processes: Alternate synthesis approaches
session 24: Lecture 24 : Counting function of Bernoulli random processes
session 25: Lecture 25 : Operations on Bernoulli random processes, and summary
part 6: Week 6
session 26: Lecture 26 : Foundations of continuous-time Poisson random processes
session 27: Lecture 27 : Poisson counting processes: Dynamical system approach, counting function
session 28: Lecture 28 : Bernoulli approximation of Poisson processes, Key properties and illustrations via counting functions of Poisson counting processes
session 29: Lecture 29 : Operations on Poisson counting processes, Illustrative examples
session 30: Lecture 30 : Illustrative examples involving Poisson counting processes, summary, and comparison of Bernoulli and Poisson counting processes.
part 7: Week 7
session 31: Lecture 31 : Continuous-time Markov Chains (CTMCs): Introduction
session 32: Lecture 32 : CTMCs Foundations 1: Formal definitions of important quantities associated with CTMCs
session 33: Lecture 33 : CTMCs Foundations 2: Transition rates, Generator, Embedded chains
session 34: Lecture 34 : CTMCs via a sequence of DTMCs
session 35: Lecture 35 : Birth-Death CTMCs: Foundations
part 8: Week 8
session 36: Lecture 36 : Birth-Death CTMCs: Illustrations
session 37: Lecture 37 : CTMCs: A re-look using first principles approach (I)
session 38: Lecture 38 : CTMCs: A re-look using first principles approach (II)
session 39: Lecture 39 : Transient analysis of CTMCs
session 40: Lecture 40 : Steady state analysis of CTMCs, Reversibility, birth-death chains and reversibility
part 9: Week 9
session 41: Lecture 41 : Renewal process: Foundations, examples, applications
session 42: Lecture 42 : Counting function of Renewal processes
session 43: Lecture 43 : Renewal function and Elementary renewal theorem
session 44: Lecture 44 : CLT for Renewal processes, Renewal reward theorem, Illustration via age of renewal
session 45: Lecture 45 : Renewal process: Illustrations and extensions
part 10: Week 10
session 46: Lecture 46 : Queuing theory: Foundations, applications, Illustrative example via timing diagram
session 47: Lecture 47 : Discrete-time Queues: Geo/Geo/1 queues
session 48: Lecture 48 : Continuous-time Queues: M/M/* queues
session 49: Lecture 49 : Delay models and delay analysis in Queueing theory
session 50: Lecture 50 : Queueing Theory: General queues, Burke's theorem, Tandem queues, examples
part 11: Week 11
session 51: Lecture 51 : Introduction to Brownian Motion and Random Walks
session 52: Lecture 52 : Properties and Joint Distributions of Brownian Motion
session 53: Lecture 53 : White Noise and Stochastic Integrals
session 54: Lecture 54 : Gaussian Processes and Brownian Bridge
session 55: Lecture 55 : Stationary Processes and Random Telegraph Signal
part 12: Week 12
session 56: Lecture 56 : Second-Order Stationarity and Auto-Regressive Processes
session 57: Lecture 57 : Linear Systems and Spectral Density
session 58: Lecture 58 : Pricing Stock Options & Arbitrage Theorem
session 59: Lecture 59 : Martingales and Geometric Brownian Motion
session 60: Lecture 60 : Black-Scholes Formula & Jump Processes

Catalogue records

nptel: 111105901 (manifestation)
nptel_video: 111105901 (manifestation)