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Mini-workshop: Stochastic differential equations: regularity and numerical analysis in finite and infinite dimensions. Abstracts from the mini-workshop held February 5–11, 2017. (English) Zbl 1390.00100

Summary: 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.

MSC:

00B05 Collections of abstracts of lectures
00B25 Proceedings of conferences of miscellaneous specific interest
65C30 Numerical solutions to stochastic differential and integral equations
65C35 Stochastic particle methods
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
65N75 Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs
60-06 Proceedings, conferences, collections, etc. pertaining to probability theory
65-06 Proceedings, conferences, collections, etc. pertaining to numerical analysis
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
65M75 Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs
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