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Adaptive step-size control for global approximation of SDEs driven by countably dimensional Wiener process.

Authors :
Stępień, Łukasz
Source :
Numerical Algorithms; Aug2024, Vol. 96 Issue 4, p1699-1725, 27p
Publication Year :
2024

Abstract

In this paper, we deal with the global approximation of solutions of stochastic differential equations (SDEs) driven by countably dimensional Wiener process. Under certain regularity conditions imposed on the coefficients, we show lower bounds for exact asymptotic error behaviour. For that reason, we analyse separately two classes of admissible algorithms: based on equidistant, and possibly not equidistant meshes. Our results indicate that in both cases, decrease of any method error requires significant increase of the cost term, which is illustrated by the product of cost and error diverging to infinity. This is, however, not visible in the finite-dimensional case. In addition, we propose an implementable, path-independent Euler algorithm with adaptive step-size control, which is asymptotically optimal among algorithms using specified truncation levels of the underlying Wiener process. Our theoretical findings are supported by numerical simulation in Python language. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
10171398
Volume :
96
Issue :
4
Database :
Complementary Index
Journal :
Numerical Algorithms
Publication Type :
Academic Journal
Accession number :
178417038
Full Text :
https://doi.org/10.1007/s11075-023-01682-y