Mercerian and Tauberian theorems with applications

井上和宾汉发展了他们自己提出的比率Mercerian定理。特别地，他们证明了系统的比率Mercerian定理可以用来证明各种Tauberian定理。例如，他们用这一理论证明了边界情况下一般核的陶伯利亚定理。他们还利用这一技巧证明了一些算术和的Tauberian和Mercerian定理。Inoue利用他介绍的过去和将来的方法证明了平稳时间序列的部分自相关函数的表示定理。利用表示定理，确定了FARIMA过程的部分自相关函数的渐近性，这是一种流行的参数长记忆模型。他们为这个模型发展了一种理论。特别是，他们给出了具有这种风险资产的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.