Approximating and Simulating Multivalued Stochastic Differential Equations

Lépingle, Dominique; Thao, Nguyen Thi

doi:10.1515/156939604777303244

Cited by 5 publications

(2 citation statements)

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“…In [14,52] related results have been derived for multivalued stochastic evolution equations in infinite dimensions. The numerical analysis for MSDEs has also been considered in [3,26,43,54,56]. However, these papers differ from the present paper in terms of the considered numerical methods, the imposed conditions, or the obtained order of convergence.…”

Section: Introductionmentioning

confidence: 99%

Error estimates of the backward Euler–Maruyama method for multi-valued stochastic differential equations

et al. 2021

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In this paper we derive error estimates of the backward Euler–Maruyama method applied to multi-valued stochastic differential equations. An important example of such an equation is a stochastic gradient flow whose associated potential is not continuously differentiable but assumed to be convex. We show that the backward Euler–Maruyama method is well-defined and convergent of order at least 1/4 with respect to the root-mean-square norm. Our error analysis relies on techniques for deterministic problems developed in Nochetto et al. (Commun Pure Appl Math 53(5):525–589, 2000). We verify that our setting applies to an overdamped Langevin equation with a discontinuous gradient and to a spatially semi-discrete approximation of the stochastic p-Laplace equation.

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Section: Introductionmentioning

confidence: 99%

Error estimates of the backward Euler–Maruyama method for multi-valued stochastic differential equations

et al. 2021

View full text Add to dashboard Cite

show abstract

“…In [14,51] related results have been derived for multi-valued stochastic evolution equations in infinite dimension. The numerical analysis for MSDEs has also been considered in [3,26,42,53,55]. However, these papers differ from the present paper in terms of the considered numerical methods, the imposed conditions, or the obtained order of convergence.…”

Section: Introductionmentioning

confidence: 99%

Error estimates of the backward Euler-Maruyama method for multi-valued stochastic differential equations

Eisenmann,

Kovács,

Kruse

et al. 2019

Preprint

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In this paper, we derive error estimates of the backward Euler-Maruyama method applied to multi-valued stochastic differential equations. An important example of such an equation is a stochastic gradient flow whose associated potential is not continuously differentiable, but assumed to be convex. We show that the backward Euler-Maruyama method is well-defined and convergent of order at least 1/4 with respect to the root-mean-square norm. Our error analysis relies on techniques for deterministic problems developed in [Nochetto, Savaré, and Verdi, Comm. Pure Appl. Math., 2000]. We verify that our setting applies to an overdamped Langevin equation with a discontinuous gradient and to a spatially semi-discrete approximation of the stochastic p-Laplace equation.

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2013

Non‐smooth Deterministic or Stochastic Discrete Dynamical Systems

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Approximating and Simulating Multivalued Stochastic Differential Equations

Cited by 5 publications

References 20 publications

Error estimates of the backward Euler–Maruyama method for multi-valued stochastic differential equations

Error estimates of the backward Euler–Maruyama method for multi-valued stochastic differential equations

Error estimates of the backward Euler-Maruyama method for multi-valued stochastic differential equations

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