| Title | On the simulation of iterated Itô integrals |
| Authors | Magnus Wiktorsson, Tobias Rydén |
| Alternative Location | http://dx.doi.org/10.1016/S..., Restricted Access |
| Publication | Stochastic Processes and their Applications |
| Year | 2001 |
| Volume | 91 |
| Issue | 1 |
| Pages | 151 - 168 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Elsevier Science |
| Abstract English | We consider algorithms for simulation of iterated Itô integrals with<br> application to simulation of stochastic differential equations. The<br> fact that the iterated Itô integral<br> I_{ij}(t_n,t_n+h)=\int_{t_n}^{t_n+h} \int_{t_n}^{s} dW_{i}(u)dW_{j}(s)<br> conditioned on W_i(t_n+h)-W_i(t_n) and W_j(t_n+h)-W_j(t_n), has an<br> infinitely divisible distribution is utilised for the simultaneous<br> simulation of $I_{ij}(t_n,t_n+h)$,W_{i}(t_n+h)-W_{i}(t_n) and<br> W_j(t_n+h)-W_j(t_n). Different simulation methods for the iterated<br> Itô integrals are investigated. We show mean square convergence rates<br> for approximations of shot-noise type and asymptotic normality of the<br> remainder of the approximations. This together with the fact that the<br> conditional distribution of I_{ij}(t_n,t_n+h), apart from an additive<br> constant, is a Gaussian variance mixture is used to achieve an<br> improved convergence rate. This is done by a coupling method for the<br> remainder of the approximation. |
| Keywords | Iterated Itô integral, Infinitely divisible distribution, Multi-dimensional stochastic differential equation, Numerical approximation, Class G distribution, Variance mixture, Coupling, |
| ISBN/ISSN/Other | ISSN: 0304-4149 |
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