Article ID Journal Published Year Pages File Type
472139 Computers & Mathematics with Applications 2012 14 Pages PDF
Abstract

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 equation which give the equivalence of the kernel lying in this class of functions and the solution lying in this class of functions. Some specific examples are examined. In particular, this theory is used to provide a counterexample to a result regarding the rate of decay of the auto-covariance function of an ARCH(∞) process.

Related Topics
Physical Sciences and Engineering Computer Science Computer Science (General)
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