Picture of smart phone in human hand

World leading smartphone and mobile technology research at Strathclyde...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by University of Strathclyde researchers, including by Strathclyde researchers from the Department of Computer & Information Sciences involved in researching exciting new applications for mobile and smartphone technology. But the transformative application of mobile technologies is also the focus of research within disciplines as diverse as Electronic & Electrical Engineering, Marketing, Human Resource Management and Biomedical Enginering, among others.

Explore Strathclyde's Open Access research on smartphone technology now...

A-stability and stochastic mean-square stability

Higham, D.J. (2000) A-stability and stochastic mean-square stability. BIT Numerical Mathematics, 40 (2). pp. 404-409. ISSN 0006-3835

Full text not available in this repository. Request a copy from the Strathclyde author

Abstract

This note extends and interprets a result of Saito and Mitsui [SIAM J. Numer. Anal., 33 (1996), pp. 2254-2267] for a method of Milstein. The result concerns mean-square stability on a stochastic differential equation test problem with multiplicative noise. he numerical method reduces to the Theta Method on deterministic problems. Saito and Mitsui showed that the deterministic A-stability property of the Theta Method does not carry through to the mean-square context in general, and gave a condition under which unconditional stability holds. The main purpose of this note is to emphasize that the approach of Saito and Mitsui makes it possible to quantify precisely the point where unconditional stability is lost in terms of the ratio of the drift (deterministic) and diffusion (stochastic) coefficients. This leads to a concept akin to deterministic A(alpha)-stability that may be useful in the stability analysis of more general methods. It is also shown that mean-square A-stability is recovered if the Theta Method parameter is increased beyond its normal range to the value 3/2.