Applied Probability

1. Front Matter

   Pages i-xiii

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2. Independent Random Sequences

   • Valérie Girardin, Nikolaos Limnios

   Pages 1-57

3. Conditioning and Martingales

   • Valérie Girardin, Nikolaos Limnios

   Pages 59-111

4. Markov Chains

   • Valérie Girardin, Nikolaos Limnios

   Pages 113-173

5. Continuous Time Stochastic Processes

   • Valérie Girardin, Nikolaos Limnios

   Pages 175-214

6. Markov and Semi-Markov Processes

   • Valérie Girardin, Nikolaos Limnios

   Pages 215-252

7. Back Matter

   Pages 253-260

   PDF

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

“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)

• Laboratoire de Mathématiques Nicolas Oresme, Université de Caen Normandie, Caen, France

  Valérie Girardin

• Laboratoire de Mathématiques Appliquées de Compiègne, Université de Technologie de Compiègne, Compiègne, France

  Nikolaos Limnios

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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