STOCHASTIC PROCESSES & APPLIED PROBABILITY: A Second Course: Renewal, Martingales, and Stochastic Calculus Volume 2

By Mir Hossain

Master stochastic processes beyond the basics-with clarity, rigor, and real understanding.

Stochastic Processes & Applied Probability: Volume 2 is a carefully structured second course designed for college and university students, engineers, quantitative analysts, and self-learners ready to move beyond introductory probability and Markov chains into the deeper mathematics of stochastic modeling.

Building directly on foundational probability and stochastic-process concepts, this volume develops the theory and applications of renewal processes, martingales, Brownian motion, stochastic calculus, stochastic differential equations, diffusion models, filtering, and simulation in a clear and accessible style.

Unlike many advanced probability texts that assume heavy mathematical maturity and skip intermediate reasoning, this book emphasizes step-by-step learning, intuition, and mastery through worked examples while maintaining mathematical rigor.

Inside this volume, you will learn:

- Renewal theory and long-run stochastic behavior
- Renewal functions and the elementary renewal theorem
- Age, residual life, and the inspection paradox
- Martingales and conditional expectation as working tools
- Filtrations, stopping times, and optional stopping
- Martingale convergence and inequalities
- Brownian motion and sample-path behavior
- The It integral and stochastic integration
- It 's formula and stochastic calculus
- Stochastic differential equations (SDEs)
- Diffusions and the Fokker-Planck equation
- Hidden Markov models and filtering methods
- Stochastic simulation and computational probability

This book features:

Clear explanations with minimal unnecessary abstraction
Fully worked examples throughout
Diagnostic reviews and prerequisite checks
Common-trap and mistake-prevention sections
Practice, Apply, and Challenge problem sets
Step-by-step solutions
Formula summaries and reference material
Self-study and classroom-friendly organization

Whether you are studying probability, applied mathematics, statistics, quantitative finance, machine learning, operations research, engineering, or stochastic modeling, this book provides a rigorous yet approachable pathway into modern stochastic processes and applied probability.

Volume 2 continues the journey from foundational stochastic models to the powerful tools used in contemporary science, engineering, finance, and data-driven systems.

• Format: Paperback
• Language: English
• ISBN: B0H3Q7Y6WT
• ISBN13: 9798199634793
• Release Date: June 2026
• Publisher: Independently published
• Length: 162 Pages
• Weight: 0.50 lbs.
• Dimensions: 9.0" x 0.4" x 6.0"