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Documents Leobacher, Gunther 2 résultats

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In the first part, we briefly recall the theory of stochastic differential equations (SDEs) and present Maruyama's classical theorem on strong convergence of the Euler-Maruyama method, for which both drift and diffusion coefficient of the SDE need to be Lipschitz continuous.

65C05 ; 91G60 ; 60H10

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Stochastic differential equations - Leobacher, Gunther (Auteur de la Conférence) | CIRM H

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In the second part we show how the classical result can be used also for SDEs with drift that may be discontinuous and diffusion that may be degenerate. In that context I will present a concept of (multidimensional) piecewise Lipschitz drift where the set of discontinuities is a sufficiently smooth hypersurface in the multi-dimensional euclidean space. We discuss geometric properties of the set of discontinuities that are needed to transfer the convergence result from the Lipschitz case to the piecewise Lipschitz case.[-]
In the second part we show how the classical result can be used also for SDEs with drift that may be discontinuous and diffusion that may be degenerate. In that context I will present a concept of (multidimensional) piecewise Lipschitz drift where the set of discontinuities is a sufficiently smooth hypersurface in the multi-dimensional euclidean space. We discuss geometric properties of the set of discontinuities that are needed to transfer the ...[+]

65C05 ; 91G60 ; 60H10

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