An Introduction to Stochastic Modeling
- 5th Edition - January 20, 2026
- Latest edition
- Authors: Gabriel Lord, Cónall Kelly
- Language: English
An Introduction to Stochastic Modeling, Fifth Edition bridges the gap between basic probability and an intermediate level course in stochastic processes, serving as the founda… Read more
An Introduction to Stochastic Modeling, Fifth Edition bridges the gap between basic probability and an intermediate level course in stochastic processes, serving as the foundation for either a one-semester or two-semester course in stochastic processes for students familiar with elementary probability theory and calculus. The objectives are to introduce students to the standard concepts and methods of stochastic modeling, to illustrate the rich diversity of applications of stochastic processes in the applied sciences, and to provide an integrated treatment of theory, applications and practical implementation. A well-regarded resource for many years, the text is an ideal foundation for a broad range of students.
- Explores realistic applications from a variety of disciplines, including biological, chemical, physical, engineering, and financial examples
- Presents a completely new treatment of modeling with stochastic differential equations, and expanded coverage of Brownian motion and martingale processes
- New applications of Markov chains to the simulation of chemical reactions via the Gillespie algorithm and to Bayesian inference via the Metropolis-Hastings algorithm
- Provides extensive end-of-section exercises sets with answers, as well as numerical illustrations
- Each chapter concludes with a section focusing on computational examples, code, and exercises that will empower students to explore concepts in a practical way
- Offers online support, sample code and solutions to coding problems for instructors, and electronic access to sample Python code for students
Upper-level undergraduate and graduate students in one-semester stochastic processes and stochastic modeling courses; assumes some background with advanced mathematics, probability theory, and calculus
1. Introduction
2. Conditional Probability and Conditional Expectation
3. Markov Chains: Introduction
4. The Long Run Behavior of Markov Chains
5. Poisson Processes
6. Continuous Time Markov Chains
7. Renewal Phenomena
8. Queueing Systems
9. Brownian Motion and Related Processes
10. Modeling Using Stochastic Differential Equations
2. Conditional Probability and Conditional Expectation
3. Markov Chains: Introduction
4. The Long Run Behavior of Markov Chains
5. Poisson Processes
6. Continuous Time Markov Chains
7. Renewal Phenomena
8. Queueing Systems
9. Brownian Motion and Related Processes
10. Modeling Using Stochastic Differential Equations
- Edition: 5
- Latest edition
- Published: January 20, 2026
- Language: English
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Gabriel Lord
Gabriel J. Lord is Professor of Applied Analysis at Radboud University Nijmegen in the Netherlands since 2019. Prior to this, he was a Professor
at the Maxwell Institute in Edinburgh, UK which he joined after a couple of years in industry at the National Physical Laboratory, UK. With over
25 years teaching experience he has been giving lectures on elements of stochastic modeling for the last twenty years. He has co-authored Stochastic Methods in Neuroscience and An Introduction to Computational Stochastic PDEs. His research is in applied and computational mathematics and in particular
for stochastic systems and models.
Affiliations and expertise
Professor of Applied Analysis, Radboud University Nijmegen, NetherlandsCK
Cónall Kelly
Cónall Kelly is Senior Lecturer (Associate Professor) of Financial Mathematics and Chair of the BSc Financial Mathematics and Actuarial Science degree at University College Cork in Ireland. He has taught courses in stochastic analysis and modeling for over 15 years and is the author of the textbook Computation and Simulation for Finance: An Introduction with Python. His research focuses on the qualitative dynamics of stochastic difference and differential equations, the analysis of numerical methods for stochastic systems, and applications in finance and biology.
Affiliations and expertise
Senior Lecturer of Financial Mathematics at University College Cork, Ireland