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We present a new pathwise approximation scheme for stochastic differential equations driven by multidimensional Brownian motion which does not require the simulation of L\'{e}vy area and has a Wasserstein convergence rate better than the Euler scheme's strong error rate of $O(\sqrt{h})$, where $h$ is the step-size.
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Strong and weak divergence in finite time of Euler’s method for stochastic differential equations with non-globally Lipschitz continuous coefficients
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Large deviations and support theorem for diffusion processes via rough paths
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Stochastic Hamiltonian systems: exponential convergence to the invariant measure, and discretization by the implicit Euler scheme
D. Talay · 2002
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On the importance of the Lévy area for studying the limits of functions of converging stochastic processes. Application to homogenization
A. Lejay and T.J. Lyons · 2003
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F. Malrieu · 2003
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Integrability and tail estimates for Gaussian rough differential equations
T. Cass, C. Litterer, and T.J. Lyons · 2013
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Evolving communities with individual preferences
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KMT theory applied to approximations of SDE
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Pathwise approximation of stochastic differential equations using coupling
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A course on rough paths
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Talagrand’s transportation-cost inequality and applications to (rough) path spaces
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The theory of rough paths via one-forms and the extension of an argument of Schwartz to RDEs
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