On Halanay-type analysis of exponential stability for the theta-Maruyama method for stochastic delay differential equations
dc.contributor.author | Baker, Christopher T. H. | |
dc.contributor.author | Buckwar, Evelyn | |
dc.date.accessioned | 2017-06-15T17:38:23Z | |
dc.date.available | 2017-06-15T17:38:23Z | |
dc.date.created | 2005-11-03 | |
dc.date.issued | 2005-11-03 | |
dc.identifier.issn | 0863-0976 | |
dc.identifier.uri | http://edoc.hu-berlin.de/18452/3238 | |
dc.description.abstract | 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)). | eng |
dc.language.iso | eng | |
dc.publisher | Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik | |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.subject | asymptotic and exponential stability | eng |
dc.subject | stochastic delay differential \& difference equations | eng |
dc.subject | Halanay-type inequalities | eng |
dc.subject | theta-Maruyama scheme | eng |
dc.subject.ddc | 510 Mathematik | |
dc.title | On Halanay-type analysis of exponential stability for the theta-Maruyama method for stochastic delay differential equations | |
dc.type | book | |
dc.identifier.urn | urn:nbn:de:kobv:11-10052206 | |
dc.identifier.doi | http://dx.doi.org/10.18452/2586 | |
local.edoc.pages | 8 | |
local.edoc.type-name | Buch | |
local.edoc.container-type | series | |
local.edoc.container-type-name | Schriftenreihe | |
local.edoc.container-year | 2004 | |
dc.identifier.zdb | 2075199-0 | |
bua.series.name | Preprints aus dem Institut für Mathematik | |
bua.series.issuenumber | 2004,14 |