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Stochastic Differential Equations with YUIMA2023VT
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Course plan
No of lectures
ca 10
Recommended for
PhD students of statistics, mathematics, computer science (with mathematical interest)
The course was last given
at LiU never, but in 2019 at Brixen-Bressanone
Goals
- teach simulation and inference methods for SDEs
- make students familiar with the YUIMA R package
Prerequisites
R, knowledge of probability and statistics
Organization
The course will be run by guest lecturers from Italy, Japan and Switzerland. STIMA is organizing this SDE school.
Content
Stochastic Calculus
Diffusion processes
Poisson process
Levy processes
Model selection
YUIMA R package
Literature
Stefano M. Iacus, Nakahiro Yoshida, Simulation and Inference for Stochastic Processes with YUIMA, Springer, 2018
Lectures
DAY 1 (Mar 21)
10:45-11:30 Introduction to stochastic calculus I (stochastic processes,
Brownian motion, labo with R) [without YUIMA]
13:00-14:15 Introduction to stochastic calculus II (stochastic integral and
SDE, labo with R) [demonstration with R, without YUIMA]
14:25-14:50 What can we do with YUIMA? [Overview of modeling and prediction
with YUIMA]
DAY 2 (Mar 22)
09:00-10:15 Simulation of diffusion processes I (Euler-Maruyama approximation
and introduction to YUIMA: yuima object, simulation, plot, Black-Scholes model,
labo)
10:30-11:30 Simulation of diffusion processes II (simulation of various
models for illustrations)
13:00-14:00 Labo (simulation with YUIMA) [invariant measure, LLN and CLT for
a diffusion process]
14:15-15:30 Poisson process and Compound Poisson processes (introduction,
simulation, labo)
DAY 3 (Mar 23)
09:00-10:15 Inference for diffusion processes I (QMLE) [method, labo]
10:30-11:30 Inference for diffusion processes II (quasi-Bayes estimation)
[method, labo]
13:00-14:45 Model selection for diffusion processes [concept, method, labo:
find the true model with given data]
15:00-16:00 YUIMA GUI
DAY 4 (Mar 24)
09:00-10:00 Levy processes and Levy driven SDE I (theoretical background and
some examples)
10:30-11:30 Levy processes and Levy driven SDE II (simulation in YUIMA)
Examination
Hand-in assignment
Examiner
Krzysztof Bartoszek
Credits
3
Comments
This SDE school has been run previously:
https://yuimaproject.com/yss2019/
The lectures/labs will be run by guest lecturers from a number of Italian,
Japanese, and Swiss institutions who will visit Linkoping for this purpose.
This course was originally meant to run in spring 2020, but was cancelled due
to the imposed travel/gathering restrictions. Hence, there is always the risk
that some travel restrictions will be imposed and we will have to cancel again
in 2022. The course will also be open to outside of LiU students.
Page responsible: Director of Graduate Studies
