Theory and Simulation of Random Phenomena
Mathematical Foundations and Physical Applications
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Beschreibung
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 typically are presented in textbooks that require a very strong mathematical background. Second, while leading the reader on this journey, it aims to impart the knowledge needed in order to develop algorithms that simulate realistic physical systems. Connections with several fields of pure and applied physics, from quantum mechanics to econophysics, are provided. Furthermore, the inclusion of fully solved exercises will enable the reader to learn quickly and to explore topics not covered in the main text. The book will appeal especially to graduate students wishing to learn how to simulate physical systems and to deepen their knowledge of the mathematical framework, which has very deep connections with modern quantum field theory.
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 typically are presented in textbooks that require a very strong mathematical background. Second, while leading the reader on this journey, it aims to impart the knowledge needed in order to develop algorithms that simulate realistic physical systems. Connections with several fields of pure and applied physics, from quantum mechanics to econophysics, are provided. Furthermore, the inclusion of fully solved exercises will enable the reader to learn quickly and to explore topics not covered in the main text. The book will appeal especially to graduate students wishing to learn how to simulate physical systems and to deepen their knowledge of the mathematical framework, which has very deep connections with modern quantum field theory.
Guides the reader step by step from basic probability theory to advanced topics like stochastic differential equations Teaches the reader how to implement his/her own algorithms for the study of physical systems Provides connections with several fields of pure and applied physics, from quantum mechanics to econophysics Includes fully solved exercises, allowing the reader to learn quickly and to explore topics not covered in the main text
Autor*in
Ettore Vitali
Themen in »Theory and Simulation of Random Phenomena«
Computational Physics graduate textbook Stochastic differential equations and applications Brownian motion Markov chains Applications to Mathematical Statistics Conditional expectations in probability theory Random variables and simulation Quantum statistics