A second-order weak approximation of SDEs using a Markov chain without Lévy area simulation

Yamada Toshihiro () and Yamamoto Kenta ()
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Yamada Toshihiro: Hitotsubashi University, Tokyo, Japan
Yamamoto Kenta: MUFG Bank, Tokyo, Japan

Monte Carlo Methods and Applications, 2018, vol. 24, issue 4, 289-308

Abstract: This paper proposes a new Markov chain approach to second-order weak approximations of stochastic differential equations (SDEs) driven by d-dimensional Brownian motion. The scheme is explicitly constructed by polynomials of Brownian motions up to second order, and any discrete moment-matched random variables or the Lévy area simulation method are not used. The required number of random variables is still d in one-step simulation of the implementation of the scheme. In the Markov chain, a correction term with Lie bracket of vector fields associated with SDEs appears as the cost of not using moment-matched random variables.

Keywords: Stochastic differential equations; weak approximation; Markov chain (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:mcmeap:v:24:y:2018:i:4:p:289-308:n:2

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DOI: 10.1515/mcma-2018-2024

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