Mercerian and Tauberian theorems with applications

井上和宾厄姆发展了由他们自己提出的比率理论。特别地，他们证明了系统的比例墨塞耳定理可以用来证明各种陶伯利定理。例如，他们用这个理论证明了边界情况下一般核的陶伯利定理。他们还用这种方法证明了一些算术和的陶伯利定理和墨塞耳定理。井上用他自己介绍的过去和未来方法证明了平稳时间序列偏自相关函数的表示定理。利用表征定理，确定了常用的参数长记忆模型FARIMA过程的部分自相关函数的渐近性。Inoue和Anh引入了一个具有记忆的风险资产价格动态模型。他们为这个模型发展了一个理论。特别给出了该风险资产在金融市场模型中的期权定价公式。

Inoue and Bingham developed the theory of ratio Mercerian theorems introduced by themselves. In particular, they showed that ratio Mercerian theorems for systems can be used to prove various Tauberian theorems. For example, they proved Tauberian theorems for general kernels in the boundary case using that theory. They also proved Tauberian and Mercerian theorems for some arithmetic sums using this technique.Inoue proved a representation theorem for partial autocorrelation functions of stationary time series, using the past and future method introduced by himself. Using the representation theorem, he determined the asymptotics for the partial autocorrelation functions of FARIMA processes, which are popular paremetric long-memory models.Inoue and Anh introduced a dynamic model of risky asset prices with memory. They developed a theory for the model. In particular, they gave option pricing formulas in the financial market model with this risky asset.