J. Appleby

activity

20062023

most citedNon-exponential stability and decay rates in nonlinear stochastic difference equation with unbounded noises

38 citations · 70 across the 29 of their papers we have counts for

collaborators

Showing 2012 · math.CAShow all

2 papers · 2 filters

math.CA2012

Necessary and sufficient conditions for periodic decaying resolvents in linear discrete convolution Volterra equations and applications to ARCH $(\infty)$ 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…

math.CA2012★ 2 cited

Long run behaviour of the autocovariance function of ARCH( $\infty$ ) models

John A. D. Appleby, John A. Daniels

The asymptotic properties of the memory structure of ARCH( $\infty$ ) equations are investigated. This asymptotic analysis is achieved by expressing the autocovariance function of AR…

Necessary and sufficient conditions for periodic decaying resolvents in linear discrete convolution Volterra equations and applications to ARCH(∞) processes

Long run behaviour of the autocovariance function of ARCH(∞) models

Necessary and sufficient conditions for periodic decaying resolvents in linear discrete convolution Volterra equations and applications to ARCH $(\infty)$ processes

Long run behaviour of the autocovariance function of ARCH( $\infty$ ) models