Προσομοίωση Απλού Τυχαίου Περιπάτου
Date Issued
October 9, 2024
Type
Πτυχιακή Εργασία
Abstract
This work presents the issue of simulating random processes, specifically the "Simple Random Walk." Simulation in computational systems has greatly facilitated conducting experiments on a computer and producing samples and conclusions, as it delivers results in a short time. The first chapter introduces topics in statistics and probability to smoothly familiarize the reader with the subsequent chapters. Topics such as the definition of randomness, as well as elements that form the basis of probability equations and their properties, such as the mean and variance, are discussed. In the second chapter, various probability equations that model random phenomena and processes are presented, such as the branching process, which can be related to the "Simple Random Walk" as they share similar properties in their construction. The third chapter presents mathematical techniques that explain the nature of random numbers and what distribution they follow. Additionally, some simple simulation examples are provided, with an emphasis on using specific functions that generate random outcomes, an important technique in the simulation process. In the fourth chapter, the reader enters the experimental part and the "Simple Random Walk" model, which is the main focus of this work. The theoretical model is presented, as well as the construction of the simulation model that will replicate it. Through code examples, the three dominant elements of simulation are made clear: data-sample collection, techniques for model construction, and the validation of the model, which will demonstrate to what extent the model appears to represent the real system. Finally, various results, diagrams, and images that illustrate the fit between the computational model and the real system are presented.
Subjects