•  #### Hands-On Simulation Modeling with Python #### Overview of this book

Simulation modeling helps you to create digital prototypes of physical models to analyze how they work and predict their performance in the real world. With this comprehensive guide, you'll understand various computational statistical simulations using Python. Starting with the fundamentals of simulation modeling, you'll understand concepts such as randomness and explore data generating processes, resampling methods, and bootstrapping techniques. You'll then cover key algorithms such as Monte Carlo simulations and Markov decision processes, which are used to develop numerical simulation models, and discover how they can be used to solve real-world problems. As you advance, you'll develop simulation models to help you get accurate results and enhance decision-making processes. Using optimization techniques, you'll learn to modify the performance of a model to improve results and make optimal use of resources. The book will guide you in creating a digital prototype using practical use cases for financial engineering, prototyping project management to improve planning, and simulating physical phenomena using neural networks. By the end of this book, you'll have learned how to construct and deploy simulation models of your own to overcome real-world challenges.
Preface Section 1: Getting Started with Numerical Simulation  Free Chapter
Chapter 1: Introducing Simulation Models Chapter 2: Understanding Randomness and Random Numbers Chapter 3: Probability and Data Generation Processes Section 2: Simulation Modeling Algorithms and Techniques Chapter 4: Exploring Monte Carlo Simulations Chapter 5: Simulation-Based Markov Decision Processes Chapter 6: Resampling Methods Chapter 7: Using Simulation to Improve and Optimize Systems Section 3: Real-World Applications Chapter 8: Using Simulation Models for Financial Engineering Chapter 9: Simulating Physical Phenomena Using Neural Networks Chapter 10: Modeling and Simulation for Project Management Chapter 11: What's Next? Other Books You May Enjoy # Markov chain applications

Now, let's look at a series of practical applications that can be made using Markov chains. We will introduce the problem and then analyze the Python code that will allow us to simulate how it works.

## Introducing random walks

Random walks identify a class of mathematical models used to simulate a path consisting of a series of random steps. The complexity of the model depends on the system features we want to simulate, which are represented by the number of degrees of freedom and the direction. The authorship of the term is attributed to Karl Pearson who, in 1905, first referred to the term casual walk. In this model, each step has a random direction that evolves through a random process involving known quantities that follow a precise statistical distribution. The path that's traced over time will not necessarily be descriptive of real motion: it will simply return the evolution of a variable over time. This is the reason for the widespread...