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Romberg extrapolations for numerical schemes solving stochastic differential equations

Talay, Denis / Tubaro, Luciano

AbstractLet (Xt) be the solution of a stochastic differential system. We consider the following situations: computation of $E ƒ(X t)$ by a Monte-Carlo method (for example, computation of moments of the solution); integration of $ƒ(·)$ with respect to the invariant probability law of (Xt) (when this process is ergodic); or of the upper Lyapunov exponent, by simulating a single trajectory.We propose to perform an extrapolation between approximate values due to first-order schemes; we show that this algorithm (simpler to implement than second-order schemes) provides a second-order accuracy, and we give results of numerical tests.

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Romberg extrapolations for numerical schemes solving stochastic differential equations

Talay, Denis / Tubaro, Luciano

AbstractLet (Xt) be the solution of a stochastic differential system. We consider the following situations: computation of $E ƒ(X t)$ by a Monte-Carlo method (for example, computation of moments of the solution); integration of $ƒ(·)$ with respect to the invariant probability law of (Xt) (when this process is ergodic); or of the upper Lyapunov exponent, by simulating a single trajectory.We propose to perform an extrapolation between approximate values due to first-order schemes; we show that this algorithm (simpler to implement than second-order schemes) provides a second-order accuracy, and we give results of numerical tests.

Romberg extrapolations for numerical schemes solving stochastic differential equations

Talay, Denis / Tubaro, Luciano

AbstractLet (Xt) be the solution of a stochastic differential system. We consider the following situations: computation of $E ƒ(X t)$ by a Monte-Carlo method (for example, computation of moments of the solution); integration of $ƒ(·)$ with respect to the invariant probability law of (Xt) (when this process is ergodic); or of the upper Lyapunov exponent, by simulating a single trajectory.We propose to perform an extrapolation between approximate values due to first-order schemes; we show that this algorithm (simpler to implement than second-order schemes) provides a second-order accuracy, and we give results of numerical tests.

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Title:

Romberg extrapolations for numerical schemes solving stochastic differential equations

Contributors:

Talay, Denis (author) / Tubaro, Luciano (author)

Published in:

Structural Safety ; 8 ; 143-150

Publication date:

1990-01-01

Size:

8 pages

ISSN:

DOI:

https://doi.org/10.1016/0167-4730(90)90036-O

Type of media:

Article (Journal)

Type of material:

Electronic Resource

Language:

English

Keywords:

Monte Carlo method , numerical analysis , probability distribution , random process , simulation

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