Higher Strong Order Methods for Itô SDEs on Matrix Lie Groups

02/08/2021
by   Michelle Muniz, et al.
0

In this paper we present a general procedure for designing higher strong order methods for 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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
09/25/2019

Runge-Kutta Lawson schemes for stochastic differential equations

In this paper, we present a framework to construct general stochastic Ru...
research
01/21/2020

Convergence rates of the Semi-Discrete method for stochastic differential equations

We study the convergence rates of the semi-discrete (SD) method original...
research
08/24/2022

Higher-order adaptive methods for exit times of Itô diffusions

We construct a higher-order adaptive method for strong approximations of...
research
01/22/2021

Numerical Methods for Backward Stochastic Differential Equations: A Survey

Backwards Stochastic Differential Equations (BSDEs) have been widely emp...
research
07/03/2023

Linear multistep methods with repeated global Richardson

In this work, we further investigate the application of the well-known R...
research
07/08/2020

Commutator-free Lie group methods with minimum storage requirements and reuse of exponentials

A new format for commutator-free Lie group methods is proposed based on ...
research
08/16/2021

Uniformly accurate schemes for oscillatory stochastic differential equations

In this work, we adapt the micro-macro methodology to stochastic differe...

Please sign up or login with your details

Forgot password? Click here to reset