线性离散卷积Volterra方程周期衰减预解式的充要条件及其在ARCH $(\infty)$过程中的应用
Necessary and sufficient conditions for periodic decaying resolvents in linear discrete convolution Volterra equations and applications to ARCH$(\infty)$ processes
摘要：
我们定义了一类具有已知衰减率和周期涨落的函数。我们确定的线性求和卷积Volterra方程的核的条件，它给出了等价的核躺在这类功能和解决方案躺在这类功能。一些具体的例子进行了检查。特别是这个理论是用来提供一个反例的结果，关于衰减率的自协方差函数的一个随机（$\infty$）过程。
英文摘要：
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 counter--example to a result regarding the rate of decay of the auto--covariance function of an ARCH($\infty$) process.
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