Probability Theory

A Foundational Course

  • Authors
  • R.¬†P.¬†Pakshirajan

Part of the Texts and Readings in Mathematics book series (TRIM, volume 63)

Table of contents

  1. Front Matter
    Pages i-xv
  2. R. P. Pakshirajan
    Pages 1-65
  3. R. P. Pakshirajan
    Pages 66-144
  4. R. P. Pakshirajan
    Pages 145-213
  5. R. P. Pakshirajan
    Pages 214-282
  6. R. P. Pakshirajan
    Pages 283-366
  7. R. P. Pakshirajan
    Pages 367-457
  8. R. P. Pakshirajan
    Pages 458-556
  9. Back Matter
    Pages 557-564

About this book

Introduction

This book shares the dictum of J. L. Doob in treating Probability Theory as a branch of Measure Theory and establishes this relation early. Probability measures in product spaces are introduced right at the start by way of laying the ground work to later claim the existence of stochastic processes with prescribed finite dimensional distributions. Other topics analysed in the book include supports of probability measures, zero-one laws in product measure spaces, Erdos-Kac invariance principle, functional central limit theorem and functional law of the iterated logarithm for independent variables, Skorohod embedding, and the use of analytic functions of a complex variable in the study of geometric ergodicity in Markov chains. This book is offered as a text book for students pursuing graduate programs in Mathematics and or Statistics. The book aims to help the teacher present the theory with ease, and to help the student sustain his interest and joy in learning the subject.

Bibliographic information

  • DOI https://doi.org/10.1007/978-93-86279-54-5
  • Copyright Information Hindustan Book Agency (India) 2013
  • Publisher Name Hindustan Book Agency, Gurgaon
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-93-80250-44-1
  • Online ISBN 978-93-86279-54-5
  • Series Print ISSN 2366-8717
  • Series Online ISSN 2366-8725
  • About this book