Advertisement

© 2010

Theory of Stochastic Processes

With Applications to Financial Mathematics and Risk Theory

Textbook

Part of the Problem Books in Mathematics book series (PBM)

Table of contents

  1. Front Matter
    Pages i-x
  2. Dmytro Gusak, Alexander Kukush, Alexey Kulik, Yuliya Mishura, Andrey Pilipenko
    Pages 1-10
  3. Dmytro Gusak, Alexander Kukush, Alexey Kulik, Yuliya Mishura, Andrey Pilipenko
    Pages 11-19
  4. Dmytro Gusak, Alexander Kukush, Alexey Kulik, Yuliya Mishura, Andrey Pilipenko
    Pages 21-32
  5. Dmytro Gusak, Alexander Kukush, Alexey Kulik, Yuliya Mishura, Andrey Pilipenko
    Pages 33-42
  6. Dmytro Gusak, Alexander Kukush, Alexey Kulik, Yuliya Mishura, Andrey Pilipenko
    Pages 43-58
  7. Dmytro Gusak, Alexander Kukush, Alexey Kulik, Yuliya Mishura, Andrey Pilipenko
    Pages 59-70
  8. Dmytro Gusak, Alexander Kukush, Alexey Kulik, Yuliya Mishura, Andrey Pilipenko
    Pages 71-105
  9. Dmytro Gusak, Alexander Kukush, Alexey Kulik, Yuliya Mishura, Andrey Pilipenko
    Pages 107-127
  10. Dmytro Gusak, Alexander Kukush, Alexey Kulik, Yuliya Mishura, Andrey Pilipenko
    Pages 129-136
  11. Dmytro Gusak, Alexander Kukush, Alexey Kulik, Yuliya Mishura, Andrey Pilipenko
    Pages 137-158
  12. Dmytro Gusak, Alexander Kukush, Alexey Kulik, Yuliya Mishura, Andrey Pilipenko
    Pages 159-173
  13. Dmytro Gusak, Alexander Kukush, Alexey Kulik, Yuliya Mishura, Andrey Pilipenko
    Pages 175-192
  14. Dmytro Gusak, Alexander Kukush, Alexey Kulik, Yuliya Mishura, Andrey Pilipenko
    Pages 193-213
  15. Dmytro Gusak, Alexander Kukush, Alexey Kulik, Yuliya Mishura, Andrey Pilipenko
    Pages 215-228
  16. Dmytro Gusak, Alexander Kukush, Alexey Kulik, Yuliya Mishura, Andrey Pilipenko
    Pages 229-240
  17. Dmytro Gusak, Alexander Kukush, Alexey Kulik, Yuliya Mishura, Andrey Pilipenko
    Pages 241-270
  18. Dmytro Gusak, Alexander Kukush, Alexey Kulik, Yuliya Mishura, Andrey Pilipenko
    Pages 271-302
  19. Dmytro Gusak, Alexander Kukush, Alexey Kulik, Yuliya Mishura, Andrey Pilipenko
    Pages 303-313
  20. Dmytro Gusak, Alexander Kukush, Alexey Kulik, Yuliya Mishura, Andrey Pilipenko
    Pages 315-326

About this book

Introduction

This book is a collection of exercises covering all the main topics in the modern theory of stochastic processes and its applications, including finance, actuarial mathematics, queuing theory, and risk theory.

 

The aim of this book is to provide the reader with the theoretical and practical material necessary for deeper understanding of the main topics in the theory of stochastic processes and its related fields.

 

The book is divided into chapters according to the various topics. Each chapter contains problems, hints, solutions, as well as a self-contained theoretical part which gives all the necessary material for solving the problems. References to the literature are also given.

 

The exercises have various levels of complexity and vary from simple ones, useful for students studying basic notions and technique, to very advanced ones that reveal some important theoretical facts and constructions.

 

This book is one of the largest collections of problems in the theory of stochastic processes and its applications. The problems in this book can be useful for undergraduate and graduate students, as well as for specialists in the theory of stochastic processes.

Keywords

Gaussian process Markov chain Martingale Poisson process Stochastic Differential Equations Stochastic Processes diffusion process filtration finite-dimensional distribution queueing theory renewal theory stochastic process

Authors and affiliations

  1. 1.Inst. MathematicsNational Academy of Sciences of UkraineKyivUkraine
  2. 2.University of Kiev, Dept. Mechanics and MathematicsNational Taras ShevchenkoKievUkraine
  3. 3.Inst. MathematicsNational Academy of Sciences of UkraineKyivUkraine
  4. 4.University of Kiev, Dept. Mechanics and MathematicsNational Taras ShevchenkoKievUkraine
  5. 5.Inst. MathematicsNational Academy of Sciences of UkraineKyivUkraine

Bibliographic information

Industry Sectors
Pharma
Biotechnology
IT & Software
Telecommunications
Finance, Business & Banking
Electronics
Energy, Utilities & Environment
Aerospace
Oil, Gas & Geosciences
Engineering

Reviews

From the reviews:

“Chapter deals with the statistics of stochastic processes, mainly hypotheses testing, a relatively uncommon subject. … The major strength of this problem book is the breadth and depth of coverage that five experts in their respective subfields condensed in only 375 pages. … the book is a valuable addition to the literature on stochastic processes. … any course in stochastics at the advanced undergraduate or beginning to intermediate graduate level is almost sure to interest its table of contents substantially.” (Giuseppe Castellacci, Mathematical Reviews, Issue 2011 f)

“Advanced undergraduates and postgraduates in mathematics, and teaching staff at these levels. This is a book in the Springer series on Problem Books in Mathematics, presenting a series of problems … . Each of the 20 chapters in this book has a condensed outline of the topic being considered, a bibliography, the problems, and then hints or solutions to most of the problems.” (David J. Hand, International Statistical Review, Vol. 78 (3), 2010)

“This book provides a collection of more than 800 problems for the theory of stochastic processes. It is divided into 20 chapters that cover different aspects of this theory. … this compilation is new in its broadness and completeness for the theory of stochastic processes and is well suited for students in their self-studies as well as lecturers to prepare their classes in this field of probability theory.” (Claudia Hein, Zentralblatt MATH, Vol. 1189, 2010)

“Each chapter consists of a brief review of theory followed by … a list of problems, hints (for the solution of) pertaining to most of the problems in the chapter, and a section giving ‘Answers and Solutions’ for many but not necessarily all problems. … It might also be used in seminars or in advanced topics courses. … There is also a set of graphical representations of various stochastic processes. … an excellent contribution and anyone who works through the problems will be well rewarded.” (Donald E. Myers, Technometrics, Vol. 53 (3), August, 2011)