MA8109 Stokastiske prosesser i systemteori
(Stochastic Differential Equations)
Høsten/Autumn 2011
This course is
lectured in English
December 13: Exam
and Project Results
December 6: Solution to exam December 2 found below.
November 29: Exam will be given in English. Answers in Norwegian or English. No written material
allowed.
TMA 4505 Fordypningsemne: Muntlig eksamen 2. desember på rom 922 Sentralbygg 2 mellom
kl. 14 og 15:30. Ta kontakt for nærmere
avtale.
The list of students registered for
the written exam looks somewhat confusing to me. Please check your registration
before Friday morning. The exam is at Trondheim Spektrum
09:00, rooms D1 (9) and E5 (1),
November 22: Project reports shall not contain names, but
student numbers. The exam will be
carried as outlined in the message below.
November 6: There have been no reservations about the date
below. I hope the following is acceptable:
November 1: Exam date has been set to 2 December (This may
be changed if it is too inconvenient).
That would
then also be the deadline for the report.
Final lecture: Tuesday 22 November.
October 31: Sorry for not putting out the solution for
Exercise 3 as promised.
October 12: Very readable supplementary notes: L.C. Evans: An
Introduction to SDEs, UC Berkeley
October 11: Proposals for Projects 2011.
October 10: Some comments to Itô
Diffusions (Chapter 7) found below. Suggestions for projects will be available
tomorrow.
October 5: A short note about linear stochastic diff.
equations and physical Brownian motion is found below. Exercise 3 is also
available.
October3:
A new
expanded version of the note about mean-square continuous functions is found
below. The new parts should be read with some care (Not all details a checked
out).
September 6: The first exercise is found below. Will be discussed in the last lecture hour Monday 12 September.
August 23: Time
and place for lectures are found below.
Unfortunately,
Gnist is sold out for the textbook (B. Øksendal: Stochastic Differential Equations) but an order has been placed, and
it should arrive in about 2 – 3 weeks. In the meantime, parts of the book is
available at Google
books or the full book at Springer Link
Lectures:
All lectures will take place in Room
734, Sentralbygg II.
Monday: 12:15 – 14:00
Tuesday: 14:15 – 16:00
Exercises:
See below.
Lecturer:
Harald E. Krogstad, rom 734,
Sentralbygg II, tlf. 73 59 35 36,
e-post: harald.krogstad@math.ntnu.no
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Exercises |
Solutions and Comments |
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Curriculum
2011 (Final version)
Exam
2003, Problems and Solutions
Exam
2007, Problems and Solutions
Exam 2011,
Problems and Solutions
MeasureAndProbability (Version: September 2007)
Lebesgueintegralet - en innføring
(Slightly more detailed introduction for Rn in Norwegian)
Brownian
Motion (Version:
September 2009)
Brownian
Motion Overheads (Version: September, 2009)
First
steps into stochastic integration (Version: September, 2011)
Mean
Square Continuous Processes (New Version: October 3, 2011)
Martingales
and the Itô Integral (Version: September 2011)
Linear
SDE and physical Brownian motion (Version: October 2011)
Comments on Diffusion (Version: October 2011)
Kolmogorov and Fokker-Planck equations (November
2011)
Notes about Girsanov's
Theorems (November 2011)
Bernt Øksendal:
Stochastic Differential Equations (Springer, 4 – 6 utgave).
Supplementary
literature:
T. Mikosch: Elementary
Stochastic Calculus with Finance in View (World Scientific, 1998. Mange opptrykk).
http://www.worldscibooks.com/mathematics/3856.html.
Dette faget ble i sin tid startet
som et seminar av professor Henrik H. Martens. Professor Martens, som døde 12.
oktober 1993, var opptatt av å formidle matematiske metoder til resten av NTNU,
og navnet henspeiler på hvordan stokastisk analyse kan brukes innenfor
systemteori. Systemteori er ”abstrakt” ingeniør-vitenskap. De siste gangene faget har vært forelest, har
innholdet blitt hentet fra stokastiske differensialligninger.
Hvem er Kiyoshi Itô? Professor Kiyoshi Itô ble født i Japan 7. september 1915, og døde 10. november 2008. Han var Professor Emeritus ved Kyoto University. Itô utviklet teorien for stokastiske integraler og stokastiske differensialligninger i 1940 og 50-årene, men forteller selv at det gikk over ti år før omverdenen tilegnet seg og satte pris på det han hadde gjort. Han kommenterer også at han allerede som student var svært utilfreds med sannsynlighetsregningen, som ikke engang var i stand til å definere en stokastisk variabel på skikkelig måte. Dette fikk han ryddet opp i da han fikk tilgang på arbeidene til Kolmogorov og Lévy.
Norsk matematisk forening arrangerte sommeren 2005 Abel-Symposiet Stochastic Analysis and Applications, a Symposium in Honor of Kiyoshi Itô. Dessverre hadde hovedpersonen for dårlig helse til selv å delta.
(WEB-side for biografier av verdensberømte matematikere ved St Andrew-universitetet i Scotland: http://www-groups.dcs.st-and.ac.uk/~history/)
Harald E. Krogstad
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