Higher strong order methods for linear Itô SDEs on matrix Lie groups

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) me...

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Bibliographic Details
Published in:BIT 2022, Vol.62 (4), p.1095-1119
Main Authors: Muniz, Michelle, Ehrhardt, Matthias, Günther, Michael, Winkler, Renate
Format: Article
Language:English
Subjects:
Computational Mathematics and Numerical Analysis
Convergence
Differential equations
Lie groups
Mathematical analysis
Mathematics
Mathematics and Statistics
Mechanical engineering
Numeric Computing
Runge-Kutta method
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Summary: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.
ISSN:0006-3835
1572-9125
DOI:10.1007/s10543-021-00905-9