线性差分系统算子方法的几点注记

Notes on Operator Methods for Linear Difference Systems

将ρ阶线性差分方程分解为ρ个一阶线性差分方程和的形式,利用一阶线性差分方程的结果导出ρ阶线性差分方程的动态性质,从而去掉已有文献中系统是稳定的这一假设.同时,使用算子方法(包括条件期望算子和滞后算子)来讨论含预期的红利模型,实现这一目标的关键在于条件期望的平滑性的算子表述.

The authors deduce the dynamic property of pth-order linear difference equation by decomposing it into the sum of p first-order linear difference equations. Some known results are proved through operator methods without the assumption that the system is stable. The model of expected dividends is also discussed through operator methods. The crux of reaching the above targets lies in the operator expression on the smoothness of conditional expectation.