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Stochastic Processes 2

Probability Examples c-9

Stochastic Processes 2
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ISBN: 978-87-7681-525-7
1 edition
Pages : 126
Price: Free

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Summary

In this book you find the basic mathematics that is needed by engineers and university students .

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About the book

  1. Description
  2. Preface
  3. Content
  4. About the Author
  5. Embed

Description

In this book you find the basic mathematics that is needed by engineers and university students . The author will help you to understand the meaning and function of mathematical concepts. The best way to learn it, is by doing it, the exercises in this book will help you do just that.

Topics as Elementary probability calculus, density functions and stochastic processes are illustrated.

This book requires knowledge of Calculus 1 and Calculus 2.

Preface

This is the ninth book of examples from Probability Theory. The topic Stochastic Processes is so big that I have chosen to split into two books. In the previous (eighth) book was treated examples of Random Walk and Markov chains, where the latter is dealt with in a fairly large chapter. In this book we give examples of Poisson processes, Birth and death processes, Queueing theory and other types of stochastic processes.

The prerequisites for the topics can e.g. be found in the Ventus: Calculus 2 series and the Ventus: Complex Function Theory series, and all the previous Ventus: Probability c1-c7.

Unfortunately errors cannot be avoided in a first edition of a work of this type. However, the author has tried to put them on a minimum, hoping that the reader will meet with sympathy the errors which do occur in the text.

Leif Mejlbro
27th October 2009

Content

Introduction

1 Theoretical background 1.1 The Poisson process 1.2 Birth and death processes 1.3 Queueing theory in general 1.4 Queueing system of innitely many shop assistants 1.5 Queueing system of a nite number of shop assistants, and with forming of queues 1.6 Queueing systems with a nite number of shop assistants and without queues 1.7 Some general types of stochastic processes

2 The Poisson process

3 Birth and death processes

4 Queueing theory

5 Other types of stochastic processes

Index

About the Author

Leif Mejlbro was educated as a mathematician at the University of Copenhagen, where he wrote his thesis on Linear Partial Differential Operators and Distributions. Shortly after he obtained a position at the Technical University of Denmark, where he remained until his retirement in 2003. He has twice been on leave, first time one year at the Swedish Academy, Stockholm, and second time at the Copenhagen Telephone Company, now part of the Danish Telecommunication Company, in both places doing research.

At the Technical University of Denmark he has during more than three decades given lectures in such various mathematical subjects as Elementary Calculus, Complex Functions Theory, Functional Analysis, Laplace Transform, Special Functions, Probability Theory and Distribution Theory, as well as some courses where Calculus and various Engineering Sciences were merged into a bigger course, where the lecturers had to cooperate in spite of their different background. He has written textbooks to many of the above courses.

His research in Measure Theory and Complex Functions Theory is too advanced to be of interest for more than just a few specialist, so it is not mentioned here. It must, however, be admitted that the philosophy of Measure Theory has deeply in uenced his thinking also in all the other mathematical topics mentioned above.

After he retired he has been working as a consultant for engineering companies { at the latest for the Femern Belt Consortium, setting up some models for chloride penetration into concrete and giving some easy solution procedures for these models which can be applied straightforward without being an expert in Mathematics. Also, he has written a series of books on some of the topics mentioned above for the publisher Ventus/Bookboon.

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