# InfoCoBuild

## 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.