Higher strong order methods for linear Itô SDEs on matrix Lie groups
Michelle Muniz, Matthias Ehrhardt, Michael Günther, Renate Winkler
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Source: Crossref
Published: Jan 4, 2022
DOI: 10.1007/s10543-021-00905-9
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Abstract In this paper we present a general procedure for designing higher strong order methods for linear Itô stochastic differential equations on matrix Lie groups and illustrate this strategy with two novel schemes that have a strong convergence order of 1.5. Based on the Runge–Kutta–Munthe–Kaas (RKMK) method for ordinary differential equations on Lie groups, we present a stochastic version of this scheme and derive a condition such that the stochastic RKMK has the same strong convergence order as the underlying stochastic Runge–Kutta method. Further, we show how our higher order schemes can be applied in a mechanical engineering as well as in a financial mathematics setting.
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