Stochastic Differential Equations by Jesper Carlsson
Stochastic Differential Equations - Table of Contents
1. Introduction to Mathematical Models and their Analysis
2. Stochastic Integrals
3. Stochastic Differential Equations
4. The Feynman-Kac Formula and the Black-Scholes Equation
5. The Monte-Carlo Method
6. Finite Difference Methods
7. The Finite Element Method and Lax-Milgram’s Theorem
8. Optimal Control and Inverse Problems
9. Rare Events and Reactions in SDE
10. Machine Learning
11. Appendices
12. Recommended Reading
What You Will Learn in Stochastic Differential Equations
"Stochastic Differential Equations: Models and Numerics" by Jesper Carlsson, Kyoung-Sook Moon, Anders Szepessy, Ra´ul Tempone and Georgios Zouraris is a clear and academically focused introduction to mathematical models that include randomness. The book is designed mainly for students and researchers who want to understand how "stochastic processes" are used to describe real-world systems affected by noise and uncertainty. It builds intuition step by step while maintaining strong mathematical foundations.
The text explains the theory of "stochastic differential equations (SDEs)", starting from probability basics and "Brownian motion", then moving to stochastic integrals and solution concepts such as Itô calculus. Special attention is given to how randomness changes the behavior of classical differential equations. The explanations are concise, supported by examples that help readers connect theory with applications.
A key strength of the book is its focus on "numerical methods" and practical modeling. It shows how SDEs are applied in fields like physics, finance, and engineering, making it useful for both theoretical study and computational work. Overall, the book serves as a solid learning resource for understanding "random dynamical systems", combining mathematical rigor with practical relevance in a student-friendly way.
Book Details & Specifications
Title:
Stochastic Differential Equations by Jesper Carlsson
Publisher:
KTH (Kungliga Tekniska Högskolan) ROYAL INSTITUTE OF TECHNOLOGY
Year:
2019
Pages:
202
Type:
PDF
Language:
English
ISBN-10 #:
0817640290
ISBN-13 #:
978-0817640293
License:
University Educational Resource
Amazon:
Amazon
About the Author: Jesper Karlsson
The author
Jesper Karlsson
and other authors of "Stochastic Differential Equations: Models and Numerics" are a collaborative team of researchers specializing in "stochastic differential equations", "numerical analysis", and "applied mathematics". Jesper Carlsson, Kyoung-Sook Moon, Anders Szepessy, Raúl Tempone, and Georgios Zouraris bring together strong academic backgrounds and teaching experience in modeling systems influenced by randomness. Their work focuses on "stochastic modeling", "numerical methods", and "scientific computing", with applications in physics, finance, and engineering. By combining theoretical insight with practical computation, the authors are well known for making complex mathematical ideas accessible to students and researchers working in modern "computational mathematics".
Read or Downloadable Stochastic Differential Equations
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