Theory and Simulation of Random Phenomena Mathematical Foundations and Physical Applications /

• Main Authors: Vitali, Ettore (Author, http://id.loc.gov/vocabulary/relators/aut), Motta, Mario (http://id.loc.gov/vocabulary/relators/aut), Galli, Davide Emilio (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: UNITEXT for Physics,
• Subjects: Physics.; Probabilities.; Statistics .; Mathematical physics.; Mathematical Methods in Physics.; Probability Theory and Stochastic Processes.; Statistical Theory and Methods.; Mathematical Applications in the Physical Sciences.; Numerical and Computational Physics, Simulation.

The purpose of this book is twofold: first, it sets out to equip the reader with a sound understanding of the foundations of probability theory and stochastic processes, offering step-by-step guidance from basic probability theory to advanced topics, such as stochastic differential equations, which...

Table of Contents:

• 1 Review of Probability Theory
• 2 Applications to Mathematical Statistics
• 3 Conditional Probability and Conditional Expectation
• 4 Markov Chains
• 5 Sampling of Random Variables and Simulation
• 6 Brownian Motion
• 7 Introduction to Stochastic Calculus and Ito Integral
• 8 Introduction to Stochastic Differential Equations and Applications
• Bibliography
• Solutions. .