STOCHASTIC PROCESSES & APPLIED PROBABILITY: A First Course in Modeling Random Systems Volume 1

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 models

This 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.