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Article Dans Une Revue Stochastic Processes and their Applications Année : 2004

Exact approximation rate of killed hypoelliptic diffusions using the discrete Euler scheme

Résumé

We are interested in approximating a multidimensional hypoelliptic diffusion process $(X_t)_{t\geq 0}$ killed when it leaves a smooth domain $D$. When a discrete Euler scheme with time step $h$ is used, we prove under a non characteristic boundary condition that the weak error is upper bounded by $C_1\sqrt h$, generalizing the result obtained by the first author in Gobet'00 for the uniformly elliptic case. We also obtain a lower bound with the same rate $\sqrt h$, thus proving that the order of convergence is exactly $\frac 12$. This provides a theoretical explanation of the well-known bias that we can numerically observe in that kind of procedure.
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Dates et versions

hal-00102258 , version 1 (29-09-2006)

Identifiants

  • HAL Id : hal-00102258 , version 1

Citer

Emmanuel Gobet, Stéphane Menozzi. Exact approximation rate of killed hypoelliptic diffusions using the discrete Euler scheme. Stochastic Processes and their Applications, 2004, 112 (2), pp.201-223. ⟨hal-00102258⟩
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