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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.