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Stochastic Processes

Stochastic Processes. Instructor: Dr. S. Dharmaraja, Department of Mathematics, IIT Delhi. This course explains and exposits concepts of stochastic processes which they need for their experiments and research. It also covers theoretical concepts pertaining to handling various stochastic modeling. This course provides classification and properties of stochastic processes, stationary processes, discrete and continuous time Markov chains and simple Markovian queueing models. (from nptel.ac.in)

Introduction


Probability Theory Refresher
Lecture 01 - Introduction to Stochastic Processes
Lecture 02 - Introduction to Stochastic Processes (cont.)
Lecture 03 - Problems in Random Variables and Distributions
Lecture 04 - Problems in Sequences of Random Variables
Definition and Simple Stochastic Processes
Lecture 05 - Definition, Classification and Examples
Lecture 06 - Simple Stochastic Processes
Stationary and Autoregressive Processes
Lecture 07 - Stationary Processes
Lecture 08 - Autoregressive Processes
Discrete-Time Markov Chain
Lecture 09 - Introduction, Definition and Transition Probability Matrix
Lecture 10 - Chapman-Kolmogorov Equations
Lecture 11 - Classification of States and Limiting Distributions
Lecture 12 - Limiting and Stationary Distributions
Lecture 13 - Limiting Distributions, Ergodicity and Stationary Distributions
Lecture 14 - Time Reversible Markov Chain, Application of Irreducible Markov Chain in Queueing Models
Lecture 15 - Reducible Markov Chains
Continuous-Time Markov Chain
Lecture 16 - Definition, Kolmogorov Differential Equations and Infinitesimal Generator Matrix
Lecture 17 - Limiting and Stationary Distributions, Birth Death Processes
Lecture 18 - Poisson Processes
Lecture 19 - M/M/1 Queueing Model
Lecture 20 - Simple Markovian Queuing Models
Lecture 21 - Queuing Networks
Lecture 22 - Communication Systems
Lecture 23 - Stochastic Petri Nets
Martingales
Lecture 24 - Conditional Expectation and Filtration
Lecture 25 - Definition and Simple Examples
Brownian Motion and its Applications
Lecture 26 - Definition and Properties
Lecture 27 - Processes Derived from Brownian Motion
Lecture 28 - Stochastic Differential Equations
Lecture 29 - Ito Integrals
Lecture 30 - Ito Formula and its Variants
Lecture 31 - Some Important Stochastic Differential Equations and their Solutions
Renewal Processes
Lecture 32 - Renewal Function and Renewal Equation
Lecture 33 - Generalized Renewal Processes and Renewal Limit Theorems
Lecture 34 - Markov Renewal and Markov Regenerative Processes
Lecture 35 - Non-Markovian Queues
Lecture 36 - Non-Markovian Queues (cont.)
Lecture 37 - Application of Markov Regenerative Processes
Branching Processes
Lecture 38 - Galton-Watson Process
Lecture 39 - Markovian Branching Process

References
Stochastic Processes
Instructor: Dr. S. Dharmaraja, Department of Mathematics, IIT Delhi. This course explains concepts of stochastic processes.