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Calcolo
Erschienen in: Calcolo 4/2015

01.12.2015

Strong convergence and stability of backward Euler–Maruyama scheme for highly nonlinear hybrid stochastic differential delay equation

verfasst von: Shaobo Zhou

Erschienen in: Calcolo | Ausgabe 4/2015

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Abstract

In the paper, our main aim is to investigate the strong convergence and almost surely exponential stability of an implicit numerical approximation under one-sided Lipschitz condition and polynomial growth condition on the drift coefficient, and polynomial growth condition on the diffusion coefficient. After providing almost surely exponential stability and moment boundedness for the exact solution, we show that an appropriate implicit numerical method preserves boundedness of moments, and the numerical approximation converges strongly to the true solution. Moreover, we prove that the backward Euler–Maruyama approximation can share almost surely exponential stability of the exact solution for sufficiently small step size.
Nächster Artikel Quadratic mixed finite element approximations of the Monge–Ampère equation in 2D
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Metadaten
Titel
Strong convergence and stability of backward Euler–Maruyama scheme for highly nonlinear hybrid stochastic differential delay equation
verfasst von
Shaobo Zhou
Publikationsdatum
01.12.2015
Verlag
Springer Milan
Erschienen in
Calcolo / Ausgabe 4/2015
Print ISSN: 0008-0624
Elektronische ISSN: 1126-5434
DOI
https://doi.org/10.1007/s10092-014-0124-x

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