Master stochastic processes with clarity, rigor, and real-world insight.
Stochastic Processes & Applied Probability: A First Course in Modeling Random Systems - Volume 1 is a carefully structured introduction designed for upper-level undergraduate and early graduate students in mathematics, statistics, engineering, operations research, economics, and data science.
Unlike many traditional texts that are overly abstract or theorem-heavy, this book emphasizes understanding through worked examples, modeling intuition, and step-by-step problem solving.
This volume develops the mathematical foundation behind systems that evolve under uncertainty - from random walks and queueing systems to Markov chains and Brownian motion.
Inside this book you will learn:
- Probability refresher and conditioning
- Law of total probability and Bayes' theorem
- Conditional expectation and modeling intuition
- Random walks and gambler's ruin
- Generating functions and branching processes
- Discrete-time Markov chains
- State classification and long-run behavior
- Absorbing chains and first-passage analysis
- The Poisson process
- Continuous-time Markov chains
- Queueing theory and M/M systems
- Brownian motion and introductory diffusion modelsThis textbook includes:
Fully worked examples with clear step-by-step solutions
Progressive difficulty from fundamentals to applications
Diagnostic reviews and mastery checkpoints
Common-trap sections to prevent frequent mistakes
Retention reviews and cumulative practice
Complete problem solutions and answer summaries
Modeling-focused explanations that connect theory with applications
Whether you are studying stochastic processes for mathematics, engineering, data science, operations research, finance, or self-study, this book provides a practical and rigorous path into one of the most powerful areas of applied mathematics.
Learn the theory. Understand the models. Apply stochastic thinking with confidence.
