Szczegóły publikacji
Opis bibliograficzny
Optimal global approximation of SDEs with time-irregular coefficients in asymptotic setting / Paweł PRZYBYŁOWICZ // Applied Mathematics and Computation ; ISSN 0096-3003. — 2015 — vol. 270, s. 441–457. — Bibliogr. s. 456–457, Abstr.
Autor
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 91375 |
|---|---|
| Data dodania do BaDAP | 2015-09-14 |
| Tekst źródłowy | URL |
| DOI | 10.1016/j.amc.2015.08.055 |
| Rok publikacji | 2015 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Applied Mathematics and Computation |
Abstract
We investigate strong approximation of solutions of scalar stochastic differential equations (SDEs) with irregular coefficients. In Przybylowicz (2015) [23], an approximation of solutions of SDEs at a single point is considered (such kind of approximation is also called a one-point approximation). Comparing to that article, we are interested here in a global reconstruction of trajectories of the solutions of SDEs in a whole interval of existence. We assume that a drift coefficient a: [0, T] x R -> R is globally Lipschitz continuous with respect to a space variable, but only measurable with respect to a time variable. A diffusion coefficient b: [0, T] -> R is only piecewise Holder continuous with Holder exponent rho is an element of (0, 1]. The algorithm and results concerning lower bounds from Przybylowicz (2015) [23] cannot be applied for this problem, and therefore we develop a suitable new technique. In order to approximate solutions of SDEs under such assumptions we define a discrete type randomized Euler scheme. We provide the error analysis of the algorithm, showing that its error is O(n(-min{rho,1/2})). Moreover, we prove that, roughly speaking, the error of an arbitrary algorithm (for fixed a and b) that uses n values of the diffusion coefficient, cannot converge to zero faster than n(-min{rho,1/2}) as n -> +infinity. Hence, the proposed version of the randomized Euler scheme achieves the established best rate of convergence. (C) 2015 Elsevier Inc. All rights reserved.
