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- W2056967088 abstract "We consider algorithms for simulation of iterated Itô integrals with application to simulation of stochastic differential equations. The fact that the iterated Itô integralIij(tn,tn+h)=∫tntn+h∫tnsdWi(u)dWj(s),conditioned on Wi(tn+h)−Wi(tn) and Wj(tn+h)−Wj(tn), has an infinitely divisible distribution utilised for the simultaneous simulation of Iij(tn,tn+h), Wi(tn+h)−Wi(tn) and Wj(tn+h)−Wj(tn). Different simulation methods for the iterated Itô integrals are investigated. We show mean-square convergence rates for approximations of shot-noise type and asymptotic normality of the remainder of the approximations. This together with the fact that the conditional distribution of Iij(tn,tn+h), apart from an additive constant, is a Gaussian variance mixture used to achieve an improved convergence rate. This is done by a coupling method for the remainder of the approximation." @default.
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- W2056967088 date "2001-01-01" @default.
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- W2056967088 title "On the simulation of iterated Itô integrals" @default.
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- W2056967088 doi "https://doi.org/10.1016/s0304-4149(00)00053-3" @default.
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