Evelyn Buckwar, Conall Kelly, Alexandra Rodkina, Gregory Berkolaiko,
"Almost sure asymptotic stability analysis of the Theta-Maruyama method applied to a test system with stabilising and destabilising stochastic perturbations"
, in LMS Journal of Computation and Mathematics, Vol. 15, Cambridge University Press, Seite(n) 71-83, 2012, ISSN: 1461-1570
Original Titel:
Almost sure asymptotic stability analysis of the Theta-Maruyama method applied to a test system with stabilising and destabilising stochastic perturbations
Sprache des Titels:
Englisch
Original Kurzfassung:
We perform an almost sure linear stability analysis of the Theta-Maruyama method, selecting as our test equation a two-dimensional system of Ito differential equations with diagonal drift coefficient and two independent stochastic perturbations which capture the stabilising and destabilising roles of feedback geometry in the almost sure asymptotic stability of the equilibrium solution. For small values of the constant step-size parameter, we derive close-to-sharp conditions for the
almost sure asymptotic stability and instability of the equilibrium solution of the discretisation that match those of the original test system. Our investigation demonstrates the use of a discrete
form of the Ito formula in the context of an almost sure linear stability analysis.