تقرير
Speeding up the Euler scheme for killed diffusions
| العنوان: | Speeding up the Euler scheme for killed diffusions |
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| المؤلفون: | Çetin, Umut, Hok, Julien |
| سنة النشر: | 2021 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, Mathematics - Probability |
| الوصف: | Let $X$ be a linear diffusion taking values in $(\ell,r)$ and consider the standard Euler scheme to compute an approximation to $\mathbb{E}[g(X_T)\mathbf{1}_{[T<\zeta]}]$ for a given function $g$ and a deterministic $T$, where $\zeta=\inf\{t\geq 0: X_t \notin (\ell,r)\}$. It is well-known since \cite{GobetKilled} that the presence of killing introduces a loss of accuracy and reduces the weak convergence rate to $1/\sqrt{N}$ with $N$ being the number of discretisatons. We introduce a drift-implicit Euler method to bring the convergence rate back to $1/N$, i.e. the optimal rate in the absence of killing, using the theory of recurrent transformations developed in \cite{rectr}. Although the current setup assumes a one-dimensional setting, multidimensional extension is within reach as soon as a systematic treatment of recurrent transformations is available in higher dimensions. Comment: Some typos and errors in the earlier version are corrected |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2107.03534 |
| رقم الأكسشن: | edsarx.2107.03534 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |