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ON THE ASYMPTOTIC BEHAVIOR OF THE MOMENTS OF SOLUTIONS OF STOCHASTIC DIFFERENCE EQUATIONS

    This work is supported partially by the Enterprise Ireland International Collaboration Programme (Grant number IC/2004/003). The first author is also partially supported by an Albert College Fellowship awarded by Dublin City University's Research Advisory Panel. The first and third authors also gratefully acknowledge the support of the Boole Centre for Research in Informatics, University College Cork, where the research was partly conducted.

    https://doi.org/10.1142/9789812770752_0048Cited by:0 (Source: Crossref)
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    Abstract:

    We investigate the asymptotic behavior of the α-th moment of the solution (Xn) of a stochastic difference equation with independent noises. Depending on α ∈ (0,1] and on the ratio u ↦ 2f(u)/g2(u) (where f is the intensity of the deterministic term and g is the intensity of the stochastic term), tends to 0 or to infinity. The analysis applies to a weak Euler-Maruyama approximation of a stochastic differential equation. To obtain our results we make use of an elementary lemma about the estimation of a positive continuous function from below by a positive continuous convex function.