On the simulation of iterated Itô integrals

Tobias Rydén and Magnus Wiktorsson

Stochastic Processes and their Applications, 2001, vol. 91, issue 1, 151-168

Abstract: We consider algorithms for simulation of iterated Itô integrals with application to simulation of stochastic differential equations. The fact that the iterated Itô integralconditioned 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.

Keywords: Iterated; Ito; integral; Infinitely; divisible; distribution; Multi-dimensional; stochastic; differential; equation; Numerical; approximation; Class; G; distribution; Variance; mixture; Coupling (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (5)

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