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A new algorithm for the approximation and simulation of twofold iterated stochastic integrals together with the corresponding L\'{e}vy areas driven by a multidimensional Brownian motion is proposed.
Approximate Integration of Stochastic Differential Equations
G. N. Milstein · 1975
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The commutation matrix: some properties and applications
J. R. Magnus and H. Neudecker · 1979
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Numerical solution of stochastic differential equations
P. E. Kloeden and E. Platen · 1992
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The approximation of multiple stochastic integrals
P. E. Kloeden, E. Platen, and I. W. Wright · 1992
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Random generation of stochastic area integrals
J. G. Gaines and T. J. Lyons · 1994
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Optimum bounds for the distributions of martingales in Banach spaces
I. Pinelis · 1994
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Numerical Integration of Stochastic Differential Equations
G. N. Milstein · 1995
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Gaussian Hilbert spaces
S. Janson · 1997
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Probability essentials
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A. Jentzen and M. Röckner · 2015
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A basic course in probability theory
R. Bhattacharya and E. C. Waymire · 2016
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Iterated stochastic integrals in infinite dimensions: approximation and error estimates
C. Leonhard and A. Rößler · 2019
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An Analysis of the Milstein Scheme for SPDEs without a Commutative Noise Condition
C. von Hallern and A. Rößler · 2020
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J. Pleis and A. Rößler · 2006
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Runge-Kutta methods for the strong approximation of solutions of stochastic differential equations
A. Rößler · 2010
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L p L^{p} and Pathwise Convergence of the Milstein Scheme for Stochastic Delay Differential Equations
J. Pleis · 2020
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