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This mini-course is given by Stig Larsson (Göteborg).
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The mini-course presents a survey of methods for proving strong convergence and weak convergence of numerical methods for the
stochastic heat and wave equations.
Strong convergence refers to convergence with respect to a norm, for example, mean square convergence. Proofs typically involve
representation of the error using the semigroup theory or energy estimates and using the Ito isometry or the Burkhold--Davies--Gundy
inequality.
Weak convergence involves the error in some functional of the solution. Proofs may involve representation of the weak error in
terms of the Kolmogorov equation and may use integration by parts from the Malliavin calculus.
The main part of the lectures will be concerned with the linear stochastic heat and wave equations.
As an example of a more difficult problem, we will briefly discuss the stochastic Cahn--Hilliard equation.

*Topics covered in this mini-course are*:

**Stochastic integration in Hilbert space. Stochastic evolution problem in Hilbert space. Semigroup, mild solution. Stochastic heat equation. Stochastic wave equation.
****Numerical approximation by finite elements and Euler's method. Strong convergence.
****Weak convergence. Malliavin calculus.
****Stochastic Cahn--Hilliard equation.
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#### Sponsors

This mini-course is organised by Jialin Hong and David Cohen
within the framework Joint China-Sweden Mobility Grant of the Swedish Foundation for
International Cooperation in Research and Higher Education
STINT and the National Natural Science Foundation of China
NSFC. We gratefully acknowledge its financial support.

We thank the Institute of Computational Mathematics at the Chinese Academy of Sciences (CAS) for the hospitality.

Further information can be found here.

And finally a picture from the classroom:

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Visit of a Swedish delegation at Shandong University (Jinan), Central South University (Changsha) and Hunan Normal (Changsha)
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November 13 - November 17, 2017

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Scientific event on numerical methods for stochastic partial differential equations

June 11-15, 2018, Chalmers University of Technology and the University of Gothenburg, Gothenburg

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We plan to organise four sessions on numerical methods for stochastic (partial) differential equations in the
40th Conference on Stochastic Processes and their Applications
SPA 2018. Further information will follow.
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**Contacts**

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**David Cohen

Department of Mathematics and Mathematical Statistics

Umeå universitet

SE-90187 Umeå
Annika Lang

Department of Mathematical Sciences

Chalmers University of Technology

SE-412 96 Göteborg

*Last modifications: 07.02.18*