Szczegóły publikacji
Opis bibliograficzny
Optimal approximation of stochastic integrals in analytic noise model / Andrzej KAŁUŻA, Paweł M. MORKISZ, Paweł PRZYBYŁOWICZ // Applied Mathematics and Computation ; ISSN 0096-3003. — 2019 — vol. 356, s. 74–91. — Bibliogr. s. 90–91, Abstr.
Autorzy (3)
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 120987 |
|---|---|
| Data dodania do BaDAP | 2019-04-23 |
| Tekst źródłowy | URL |
| DOI | 10.1016/j.amc.2019.03.022 |
| Rok publikacji | 2019 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Applied Mathematics and Computation |
Abstract
We study approximate stochastic Itô integration of processes belonging to a class of progressively measurable stochastic processes that are Hölder continuous in the rth mean. Inspired by increasing popularity of computations with low precision (used on Graphics Processing Units – GPUs and standard Computer Processing Units – CPUs), we introduce a suitable analytic noise model of standard noisy information about X and W. In this model we show that the upper bounds on error of the Riemann–Maruyama quadrature are proportional to n −ϱ +δ 1 +δ 2 , where n is a number of noisy evaluations of X and W, ϱ ∈ (0, 1] is a Hölder exponent of X, and δ 1 , δ 2 ≥ 0 are precision parameters for values of X and W, respectively. Moreover, we show that the error of any algorithm based on at most n noisy evaluations of X and W is at least C(n −ϱ +δ 1 ). Finally, we report numerical experiments performed on both CPU and GPU, together with some computational performance comparison between those two architectures. © 2019 Elsevier Inc.
