Joint characteristic function and simultaneous simulation of iterated Itô integrals for multiple independent Brownian motions

By M. Wiktorsson. 2001

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Antithetic Multilevel Monte Carlo Estimation for Multidimensional SDEs (2013, methodology): “However, there is no method for simulating Lévy areas with a cost per timestep similar to that of Brownian increments, apart from in dimension 2 [2, 9, 10].”
A structural analysis of asymptotic mean-square stability for multi-dimensional linear stochastic differential systems (2012, methodology): “Several methods to deal with this situation have been proposed in the literature [12, 13, 21, 22, 28, 34], see also [14] for an implementation in Matlab and simulation studies.”
Characterization of bistability for stochastic multistep methods (2010, unknown): “We refer to [28, 33] for methods to approximate iterated stochastic integrals I ti α .”
Scalable Gradients for Stochastic Differential Equations (2020, background): “These random variables are difficult to simulate and costly to approximate [83].”
Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without Lévy area simulation (2012, methodology): “However, a weakness of the Milstein discretisation is that in multiple dimensions it generally requires the simulation of iterated Itô integrals known as Lévy areas, for which there is no known efficient method except in dimension 2 [4, 17, 18].”