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Applied Stochastic Processes
Online
12 Weeks
Free Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study |
Important dates
Certificate Exam Date
Start Date : 19 Apr, 2026
Courses and Certificate Fees
| Fees Informations | Certificate Availability | Certificate Providing Authority |
|---|---|---|
| INR 1000 | yes | IIT Kharagpur |
The Syllabus
Preliminaries I
- Introduction to probability, review of distributions: Bernoulli, Binomial, Poisson, Multinomial, Exponential, Gamma, Gaussian distribution
Preliminaries II
- Conditional probability, Conditional expectation and variance, Computations with conditioning, Central limit theorem, Software demonstration of simulating discrete and continuous random variables
DTMC I
- Discrete time stochastic processes, Discrete time Markov chains, transition probabilities, Chapman-Kolmogorov equations, classification of states, Software demonstration of the concepts
DTMC II
- Limiting probabilities, Connection to Perron Frobenius Theorem, Mean time spent in transient states, Branching processes, Time reversible Markov chains, Applications
Discrete time counting processes
- Bernoulli random processes, definitions and alternate synthesis approaches via interarrivals, properties, operating on Bernoulli processes like merging and splitting, Applications to simple discrete-time queues
Continuous time counting processes
- Poisson processes, Interarrival and waiting time distributions, merging and splitting operations, order statistics, conditional distribution on arrival times, marked and compound Poisson processes, Applications
CTMC I
- Birth and Death processes, Transition probability function.
CTMC II
- Kolmogorov’s backward and forward equations, Limiting probabilities, Applications
Renewal
- definitions, examples, Limit theorems, renewal reward, Applications to reliability
Applications to Queuing theory
- basic definitions of queues and Kendall notation, analysis of M/M/X/X queues
Martingale and Brownian motion
- definition, connections to other processes, Hitting times, Gambler’s ruin problem, Brownian motion with drift, Geometric Brownian motion, White noise, Gaussian processes, Stationary and weak stationary processes
Applications
- Option pricing, risk neutral pricing, Arbitrage theorem, Black Scholes option pricing formula