© 2018

Applied Probability

From Random Sequences to Stochastic Processes


  • Presents a comprehensive course on applied stochastic processes

  • Includes a wealth of exercises with detailed solutions

  • Provides numerous examples in reliability, information theory, production, risk, and other areas

  • Builds a bridge between regular textbooks on probability theory and advanced monographs


Table of contents

  1. Front Matter
    Pages i-xiii
  2. Valérie Girardin, Nikolaos Limnios
    Pages 1-57
  3. Valérie Girardin, Nikolaos Limnios
    Pages 59-111
  4. Valérie Girardin, Nikolaos Limnios
    Pages 113-173
  5. Valérie Girardin, Nikolaos Limnios
    Pages 175-214
  6. Valérie Girardin, Nikolaos Limnios
    Pages 215-252
  7. Back Matter
    Pages 253-260

About this book


This textbook addresses postgraduate students in applied mathematics, probability, and statistics, as well as computer scientists, biologists, physicists and economists, who are seeking a rigorous introduction to applied stochastic processes. Pursuing a pedagogic approach, the content follows a path of increasing complexity, from the simplest random sequences to the advanced stochastic processes. Illustrations are provided from many applied fields, together with connections to ergodic theory, information theory, reliability and insurance. The main content is also complemented by a wealth of examples and exercises with solutions.


Probability Random sequences Random processes Markov chains Semi-Markov processes Martingales Stochastic topology Central limit theorem Law of large numbers Statistical distributions Stopping time theorem Conditional expectation Stochastic processes

Authors and affiliations

  1. 1.Laboratoire de Mathématiques Nicolas OresmeUniversité de Caen NormandieCaenFrance
  2. 2.Laboratoire de Mathématiques Appliquées de CompiègneUniversité de Technologie de CompiègneCompiègneFrance

About the authors

Valérie Girardin received her Ph.D. in Probability from the Université Paris-Sud in Orsay, France. She teaches analysis, probability and statistics to various levels of students, including future secondary school teachers in mathematics, future engineers and researchers. Her research interests include diverse aspects of stochastic processes, from theory to applied statistics, with a particular interest in information theory and biology.

Nikolaos Limnios graduated from the Aristotle University of Thessaloniki and Polytechnic School of Thesaloniki, Greece. He received his Ph.D. and his Doctorat d’Etat  from the Université de Technologie de Compiègne (UTC), France, where he is now a full professor. He teaches probability,  statistics and stochastic processes to future engineers. His research interests in stochastic processes  and statistics include Markov, semi-Markov processes, branching processes, random evolutions and their applications in biology, reliability, earthquake, population evolutions, among other topics. 


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“The primary audience of the book are students studying mathematics at a university and Ph.D. students in applied mathematics. It can also be served as a course at master’s and doctoral’s levels in applied probability. And finally, it is conceived as a support for the researchers and engineers dealing with stochastic modelling.” (Anatoliy Swishchuk, zbMATH 1434.60002, 2020)

“It is intended for students (at master or PhD level) in applied mathematics as well as researchers and engineers dealing with stochastic modeling issues. … Finally, the readers who want to get their hands on the different notions presented in the book will find at the end of each section a series of exercises with their solutions.” (Julien Poisat, Mathematical Reviews, October, 2019)