Asymptotic behaviour of a nonlinear stochastic difference equation modelling an inefficient financial market

Appleby, John A. D.; Swords, Catherine

doi:10.2969/aspm/05310011

Cited by 2 publications

(1 citation statement)

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“…The literature on asymptotically constant solutions to deterministic functional differential and Volterra equations is extensive; a recent contribution to this literature, which also gives a nice survey of results is presented in [11]. Motivation from the sciences for studying the phenomenon of asymptotically constant solutions in deterministic and stochastic functional differential or functional difference equations arise for example from the modelling of endemic diseases [14,3] or in the analysis of inefficient financial markets [8].…”

Section: Introductionmentioning

confidence: 99%

Convergence rates of the solution of a Volterra-type stochastic differential equations to a non-equilibrium limit

Appleby¹

2007

Proceedings of the 8'th Colloquium on the Qualitative Theory of Differential Equations (June 25--28, 2007, Szeged, Hungary) Edi

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This paper concerns the asymptotic behaviour of solutions of functional differential equations with unbounded delay to non-equilibrium limits. The underlying deterministic equation is presumed to be a linear Volterra integro-differential equation whose solution tends to a non-trivial limit. We show when the noise perturbation is bounded by a non-autonomous linear functional with a square integrable noise intensity, solutions tend to a non-equilibrium and non-trivial limit almost surely and in meansquare. Exact almost sure convergence rates to this limit are determined in the case when the decay of the kernel in the drift term is characterised by a class of weight functions.

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Section: Introductionmentioning

confidence: 99%

Convergence rates of the solution of a Volterra-type stochastic differential equations to a non-equilibrium limit

Appleby¹

2007

Proceedings of the 8'th Colloquium on the Qualitative Theory of Differential Equations (June 25--28, 2007, Szeged, Hungary) Edi

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Stochastic Delay Difference and Differential Equations: Applications to Financial Markets

Swords¹

2009

Irish Math. Soc. Bull.

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Asymptotic behaviour of a nonlinear stochastic difference equation modelling an inefficient financial market

Cited by 2 publications

References 8 publications

Convergence rates of the solution of a Volterra-type stochastic differential equations to a non-equilibrium limit

Convergence rates of the solution of a Volterra-type stochastic differential equations to a non-equilibrium limit

Stochastic Delay Difference and Differential Equations: Applications to Financial Markets

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