التفاصيل البيبلوغرافية
| العنوان: |
Higher strong order methods for linear Itô SDEs on matrix Lie groups. |
| المؤلفون: |
Muniz, Michelle, Ehrhardt, Matthias, Günther, Michael, Winkler, Renate |
| المصدر: |
BIT: Numerical Mathematics; Dec2022, Vol. 62 Issue 4, p1095-1119, 25p |
| مصطلحات موضوعية: |
LINEAR orderings, ORDINARY differential equations, STOCHASTIC orders, FINANCIAL engineering, SET theory |
| مستخلص: |
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. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
Complementary Index |
