Kaisa_2012_3_photo by Veikko Somerpuro

by Prof. Carlos Braumann (University of Evora, Portugal)

This course is intended as a first introduction to stochastic differential equations (SDE), focusing on the basic theoretical issues and on applications mainly in Biology, such as, to name a few, population growth (including issues as extinction), profit optimization in fisheries, individual animal growth (and profit optimization in livestock production), epidemics. SDE are basically ordinary differential equations with an additional stochastic term that allows us to handle the effect of the random environment fluctuations on the dynamics of the phenomena under study. These random perturbations are particularly significant in biological phenomena and may produce considerable deviations from the mean dynamics, as well as new qualitative features. However, such perturbations do occur also in many other areas and so SDE are quite useful tools in studying dynamical phenomena in all fields of Science and Technology. They are particularly prevalent in the modern Financial Mathematics to deal with stocks, options, return rates, etc., and, since some of the models are common to those used in Biology, we will briefly mention these other applications as well. The statistical issues of estimation, Monte Carlo simulation and prediction for SDE models will also be briefly addressed.

Enrol
1.11.2018 at 08:00 - 16.12.2018 at 23:59

Messages

Eva Kisdi's picture

Eva Kisdi

Published, 2.1.2019 at 12:42

Dear All,

instructions Carlos sent to the upcoming exam of the Stochastic differential equations course:
"You can consult the course book copy and your class notes, as well as a table of the standard
Gaussian distribution function. You can use a hand calculator. All questions have the same credit. Partial answers will be considered for partial credit. The exam duration will be 3 hours."

PS from me: bring a calculator (not a smartphone), you will need it!

Very bests,
Eva

Timetable

Here is the course’s teaching schedule. Check the description for possible other schedules.

DateTimeLocation
Mon 3.12.2018
10:15 - 12:00
Mon 3.12.2018
12:15 - 14:00
Tue 4.12.2018
10:15 - 12:00
Tue 4.12.2018
12:15 - 14:00
Wed 5.12.2018
10:15 - 12:00
Wed 5.12.2018
12:15 - 14:00
Fri 7.12.2018
10:15 - 12:00
Fri 7.12.2018
12:15 - 14:00
Mon 10.12.2018
10:15 - 12:00
Mon 10.12.2018
12:15 - 14:00
Tue 11.12.2018
10:15 - 12:00
Tue 11.12.2018
12:15 - 14:00
Wed 12.12.2018
10:15 - 12:00
Wed 12.12.2018
12:15 - 14:00
Thu 13.12.2018
10:15 - 12:00
Thu 13.12.2018
12:15 - 14:00
Fri 14.12.2018
10:15 - 12:00
Fri 14.12.2018
12:15 - 14:00

Material

As agreed, the pdf files of the slides used in the lectures have now been removed from this page. If you would like to get the slides and you were participating in the course or you are otherwise affiliated with the University of Helsinki, please contact Eva Kisdi. These files are not available for outsiders.

Conduct of the course

EXAM: open book. You'll need a calculator (not a smartphone!) and a table of the normal distribution.
Times and places: Friday 11 January 10-13 in B121 and Thursday 24 January 10-13 in CK107.
Address questions of organisation to Eva Kisdi.