Theory of Stochastic Processes

With Applications to Financial Mathematics and Risk Theory

  • Dmytro Gusak
  • Alexander Kukush
  • Alexey Kulik
  • Yuliya Mishura
  • Andrey Pilipenko

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

  • Dmytro Gusak
    • 1
  • Alexander Kukush
    • 2
  • Alexey Kulik
    • 3
  • Yuliya Mishura
    • 4
  • Andrey Pilipenko
    • 5
  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

  • DOI https://doi.org/10.1007/978-0-387-87862-1
  • Copyright Information Springer Science+Business Media, LLC 2010
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-87861-4
  • Online ISBN 978-0-387-87862-1
  • Series Print ISSN 0941-3502
  • About this book