Numerical Methods for Deterministic and Stochastic Differential Equations
Beräkningsmetoder för deterministiska och stokastiska differentialekvationer

FMN010F, 7.5 högskolepoäng

Gäller från och med: Autumn 2013
Beslutad av: FN1/Anders Gustafsson
Datum för fastställande: 2014-09-15

Allmänna uppgifter

Avdelning: Numerical Analysis
Kurstyp: Ren forskarutbildningskurs
Undervisningsspråk: English

Syfte

Stochastic differential equations are increasingly important in many cutting-edge models in physics, biochemistry and finance. The aim of the course is to give the postgraduate student a fundamental knowledge and understanding of stochastic differential equations, emphasizing the computational techniques necessary for stochastic simulation in modern applications.

Mål

Kunskap och förståelse

För godkänd kurs skall doktoranden

• have a good understanding of the difference between stochastic and deterministic equations, and of Monte Carlo methods for stochastic simulation.
• be able to analyse basic methods for stochastic differential equations, such as the Euler-Maruama and Milstein methods, and more general Runga-Kutta methods.
• have a good understanding of weak and strong convergence, and of stability theory for stochastic differential equations.
• be able to interpret stochastic differential equations and to give examples of models that include them.

Färdighet och förmåga

För godkänd kurs skall doktoranden be able to independently implement discretization schemes for stochastic differential equations and critically evaluate the results.

Kursinnehåll

The course is divided into two parts, with the first dealing with classical theory for deterministic ordinary differential equations (ODEs) and the second with theory for stochastic differential equations (SDEs). The deterministic part reviews necessary background, in particular Runge-Kutta and Rosenbrock methods. The second part gives an introduction to SDEs, and presents basic ideas and techniques used in statistical simulation, such as root mean square stability; consistency notions; and weak and strong convergence. A few applications will be studied in more detail, including pertinent problems to be solved using a computer.

Kurslitteratur

Averina, Tatjana A.: Numerical analysis of systems of ordinary and stochastic differential equations. V.S.P. International Science, 1997. ISBN 9789067642507.

Kursens undervisningsformer

Undervisningsformer: Föreläsningar, projekt

Kursens examination

Examinationsformer: Muntlig tentamen, seminarieföredrag av deltagarna
Betygsskala: Underkänd, godkänd
Examinator:

Antagningsuppgifter

Förutsatta förkunskaper: FMNN10 Numerical Methods for Differential Equations, Probability Theory.

Övrig information

The course is given if at least five postgraduate students apply. However, there may be some months' delay.

Kurstillfällesinformation

Kontaktinformation och övrigt

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