MVEX01-21-22 An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations

​Stochastic differential equations (SDEs) play a prominent role in sciences and engineering. These models have a wide range of application areas, including biology, chemistry, epidemiology, mechanics, neuroscience, and finance.

A complete understanding of the theory around SDE requires knowledge in advanced probability theory and stochastic analysis. However, it is possible to appreciate the basics of how to numerically simulate SDEs with just a background knowledge of Euler’s method for deterministic ordinary differential equations and an intuitive understanding of random variables.

The goal of the bachelor thesis is to provide students with a practical and accessible introduction to numerical methods for stochastic differential equations. This will be done by reading the article "An algorithmic introduction to numerical simulation of stochastic differential equations" and implementing various programs in matlab for instance.  

Main reference: Higham D (2001), "An algorithmic introduction to numerical simulation of stochastic differential equations", SIAM Rev.. Vol. 43(3), pp. 525-546

Rapporten skrivs på svenska.

Projektkod MVEX01-21-22
Gruppstorlek 3-4 studenter
Målgrupp GU- och Chalmersstudenter. För GU-studenter räknas projektet som ett projekt i Tillämpad matematik (MMG900/MMG920).
Projektspecifika förkunskapskrav Basic knowledge in ODE, intuitive understanding of random variables, knowledge of a scientific programming language such as matlab for example
Se respektive kursplan för allmänna förkunskapskrav. Utöver de allmänna förkunskapskraven i MVEX01 ska Chalmersstudenter ha avklarat kurser i en- och flervariabelanalys, linjär algebra och matematisk statistik.
Handledare David Cohen (031-7723021, david.cohen@chalmers.se), Annika Lang (031-7725356, annika.lang@chalmers.se)
Examinator Maria Roginskaya, Ulla Dinger
Institution Matematiska vetenskaper

Publicerad: to 29 okt 2020.