Author： Korzeniowski Andrzej
Publisher： Taylor & Francis Ltd
ISSN： 0736-2994
Source： Stochastic Analysis and Applications, Vol.26, Iss.6, 2008-11, pp. : 1267-1273
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Abstract
Long time behavior of stochastic differential equations (SDE) involves two instances of exponential mean square stability (EMS-stability). First deals with stability of the original continuous time system while the second is concerned with stability after the time step discretization. By considering a linear operator S associated with SDE, we show that the discrete system is EMS-stable if and only if S is a positive contraction on the set of symmetric positive definite matrices.
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