4 citations · 9 across the 6 of their papers we have counts for
6 papers
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…
Exact Pathwise and Mean--Square Asymptotic Behaviour of Stochastic Affine Volterra and Functional Differential Equations
John A. D. Appleby, John A. Daniels
The almost sure rate of exponential-polynomial growth or decay of affine stochastic Volterra and affine stochastic finite-delay equations is investigated. These results are achieve…
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…
A Black--Scholes Model with Long Memory
John A. D. Appleby, John A. Daniels, Katja Krol
This note develops a stochastic model of asset volatility. The volatility obeys a continuous-time autoregressive equation. Conditions under which the process is asymptotically stat…
Necessary and sufficient conditions for periodic decaying resolvents in linear discrete convolution Volterra equations and applications to ARCH processes
John A. D. Appleby, John A. Daniels
We define a class of functions which have a known decay rate coupled with a periodic fluctuation. We identify conditions on the kernel of a linear summation convolution Volterra eq…
Long run behaviour of the autocovariance function of ARCH() models
John A. D. Appleby, John A. Daniels
The asymptotic properties of the memory structure of ARCH() equations are investigated. This asymptotic analysis is achieved by expressing the autocovariance function of AR…