High Order Numerical Approximation of the Invariant Measure of Ergodic SDEs | Zendy

Assyr Abdulle | Zendy; Gilles Vilmart | Zendy; Konstantinos C. Zygalakis | Zendy

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High Order Numerical Approximation of the Invariant Measure of Ergodic SDEs

Author(s) -

Assyr Abdulle,

Gilles Vilmart,

Konstantinos C. Zygalakis

Publication year - 2014

Publication title -

siam journal on numerical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.78

H-Index - 134

eISSN - 1095-7170

pISSN - 0036-1429

DOI - 10.1137/130935616

Subject(s) - ergodic theory , invariant measure , mathematics , stochastic differential equation , invariant (physics) , measure (data warehouse) , brownian motion , integrator , order of accuracy , mathematical analysis , differential equation , numerical partial differential equations , computer science , statistics , computer network , bandwidth (computing) , database , mathematical physics

International audienceWe introduce new sufficient conditions for a numerical method to approximate with high order of accuracy the invariant measure of an ergodic system of stochastic differential equations, independently of the weak order of accuracy of the method. We then present a systematic procedure based on the framework of modified differential equations for the construction of stochastic integrators that capture the invariant measure of a wide class of ergodic SDEs (Brownian and Langevin dynamics) with an accuracy independent of the weak order of the underlying method. Numerical experiments confirm our theoretical findings

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