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math.PR2013★ 1 cited
Long Memory and Financial Market Bubble Dynamics in Affine Stochastic Differential Equations with Average Functionals
John A. D. Appleby, John A. Daniels
In this paper we consider the growth, large fluctuations and memory properties of an affine stochastic functional differential equation with an average functional where the contrib…
math.PR2012★ 2 cited
On the Admissibility of Linear Stochastic Volterra Operators
John A. D. Appleby, John A. Daniels, David W. Reynolds
Conditions guaranteeing convergence of linear stochastic Volterra operators are studied. Necessary and sufficient conditions for mean square convergence are established, while almo…