Introduction to Stochastic Processes and its Applications Lecture Note

Description

Name of Notes : – Introduction to Stochastic Processes and its Applications Lecture Note

Introduction

A stochastic process is a set of random variables indexed by time or space. Stochastic modelling is an interesting and challenging area of probability and statistics that is widely used in the applied sciences. In this course you will gain the theoretical knowledge and practical skills necessary for the analysis of stochastic systems. You will study the basic concepts of the theory of stochastic processes and explore different types of stochastic processes including Markov chains, Poisson processes and birth-and-death processes.

Non-Statistics master’s students may want to consider taking STATS 215 instead.

What you will learn

• The standard concepts and methods of stochastic modeling
• How to choose the best stochastic process for specific situations
• How to apply stochastic analysis to realistic problems

Prerequisites

• A post-calculus introductory probability course, e.g. Stanford Course STATS116
• A conferred Bachelor’s degree with an undergraduate GPA of 3.3 or better.

Topics include

• Discrete and continuous time Markov chains
• First step analysis: gambler’s ruin and successful runs
• Branching processes
• Poisson processes
• Birth-and-death processes
• Long run behavior

Course Availability

The course schedule is displayed for planning purposes – courses can be modified, changed, or cancelled. Course availability will be considered finalized on the first day of open enrollment. For quarterly enrollment dates, please refer to our graduate education section.

Modules / Lectures

• Concepts of Random walks, Markov Chains, Markov Processes
• Poisson Process and Kolmorogov equations
• Branching process, Application of Markov chains, Markov Processes with discrete and continuous state
• Renewal Processes and Theory, Limit theorems in renewal theory
• Understanding of applications of renewal theory, Stationary Process with discrete and continuous par
• Random walks and related areas
• Application of stochastic processes in queueing theory
• Application of stochastic processes in areas like scheduling
• Application of stochastic processes in areas like manufacturing
• Application of stochastic processes in areas like finance
• Application of stochastic processes in areas marketing
• Application of stochastic processes in areas of engineering and management science