Stochastic Processes: Theory for Applications
This definitive textbook provides a solid introduction to discrete and continuous stochastic processes, tackling a complex field in a way that instils a deep understanding of the relevant mathematical principles, and develops an intuitive grasp of the way these principles can be applied to modelling real-world systems. It includes a careful review of elementary probability and detailed coverage of Poisson, Gaussian and Markov processes with richly varied queuing applications. The theory and applications of inference, hypothesis testing, estimation, random walks, large deviations, martingales and investments are developed. Written by one of the world's leading information theorists, evolving over twenty years of graduate classroom teaching and enriched by over 300 exercises, this is an exceptional resource for anyone looking to develop their understanding of stochastic processes.
Why Read This Book
You will gain a rigorous, application-minded foundation in stochastic processes that directly supports work in DSP, communications, radar, and statistical signal processing. Gallager blends clear mathematical development with real-world modelling and abundant exercises so you learn both theory and how to apply it to queueing, estimation, detection, and random-process analysis.
Who Will Benefit
Graduate students and practicing engineers in communications, DSP, radar, and statistical signal processing who need a thorough, mathematically sound treatment of stochastic models and inference.
Level: Advanced — Prerequisites: Single-variable calculus, linear algebra, and a basic course in probability and random variables; familiarity with transforms (Fourier/Laplace) and signals/systems is helpful.
Key Takeaways
- Model stochastic systems using Poisson, Gaussian, and Markov process frameworks applicable to communications and radar.
- Analyze queues, renewal processes, and birth–death systems to evaluate performance metrics relevant to networking and signal processing pipelines.
- Derive and apply estimation and hypothesis-testing results for random signals, including linear estimation and detection principles.
- Apply limit theorems, martingale methods and large-deviation techniques to assess rare events and asymptotic behavior in signal-processing systems.
- Formulate and analyze random walks and their implications for spectral analysis, adaptive filtering convergence, and error processes.
Topics Covered
- 1. Review of Probability and Random Variables
- 2. Convergence, Laws of Large Numbers and Limit Theorems
- 3. Generating Functions and Transforms
- 4. Poisson and Renewal Processes
- 5. Markov Chains (Discrete-Time) and Applications
- 6. Continuous-Time Markov Processes and Birth–Death Models
- 7. Queueing Theory and Network Applications
- 8. Gaussian Processes and Spectral Representations
- 9. Linear Estimation, Prediction and Filtering
- 10. Hypothesis Testing and Detection Theory
- 11. Random Walks, Martingales and Stopping Times
- 12. Large Deviations and Asymptotic Methods
- 13. Selected Applications to Communications, DSP and Finance
Languages, Platforms & Tools
How It Compares
Compared with Ross's Stochastic Processes (more general probability text) and Papoulis & Pillai (signal-processing oriented), Gallager's book emphasizes information-theoretic and communications applications with rigorous proofs and extensive exercises.
