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European Mathematical Society Publishing House
2018-01-05 23:40:04
Oberwolfach Reports
Oberwolfach Rep.
OWR
1660-8933
1660-8941
General
10.4171/OWR
http://www.ems-ph.org/doi/10.4171/OWR
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© Mathematisches Forschungsinstitut Oberwolfach
14
2017
1
Mini-Workshop: Stochastic Differential Equations: Regularity and Numerical Analysis in Finite and Infinite Dimensions
Martin
Hutzenthaler
Universität Duisburg-Essen, Germany
Annika
Lang
Chalmers University of Technology, Göteborg and Göteborg University, Sweden
Lukasz
Szpruch
Edinburgh University, UK
Larisa
Yaroslavtseva
Universität Passau, Germany
This Mini-Workshop is devoted to regularity and numerical analysis of stochastic ordinary and partial differential equations (SDEs for both). The standard assumption in the literature on SDEs is global Lipschitz continuity of the coefficient functions. However, many SDEs arising from applications fail to have globally Lipschitz continuous coefficients. Recent years have seen a prosper growth of the literature on regularity and numerical approximations for SDEs with non-globally Lipschitz coefficients. Some surprising results have been obtained – e.g., the Euler–Maruyama method diverges for a large class of SDEs with super-linearly growing coefficients, and the limiting equation of a spatial discretization of the stochastic Burgers equation depends on whether the discretization is symmetric or not. Several positive results have been obtained. However the regularity of numerous important SDEs and the closely related question of convergence and convergence rates of numerical approximations remain open. The aim of this workshop is to bring together the main contributers in this direction and to foster significant progress.
Numerical analysis
Probability theory and stochastic processes
453
498
10.4171/OWR/2017/9
http://www.ems-ph.org/doi/10.4171/OWR/2017/9
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2
2018