Format:
1 Online-Ressource (8 Seiten)
ISSN:
0863-0976
Series Statement:
Preprints aus dem Institut für Mathematik 2004,2005,14
Content:
Using an approach that has its origins in work of Halanay, we consider stability in mean square of numerical solutions obtained from the theta-Maruyama discretization of a test stochastic delay differential equation dX(t) = {f(t) -alpha X(t) + beta X(t - tau)} {dt + {g(t) + eta X(t) + mu X (t - tau) } dW(t), interpreted in the Itô sense, where W(t) denotes a Wiener process. We focus on demonstrating that we may use techniques advanced in a recent report by Baker and Buckwar to obtain criteria for asymptotic and exponential stability, in mean square, for the solutions of the recurrence Xn+1 - Xn = theta h {fn+1 - alpha Xn+1 + beta Xn+1 - N} + + (1-theta) h {fn - alpha Xn + beta Xn-N} + sqrt{h} (gn + eta Xn + mu Xn-N) xi n (xi n in N (0,1)).
Language:
English
URN:
urn:nbn:de:kobv:11-10052206
URL:
Volltext
(kostenfrei)
Bookmarklink