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Baxter's inequality and convergence of finite predictors of multivariate stochastic processess
SummaryWe show that smoothness properties of a spectral density matrix and its optimal factor are closely related when the density satisfies theboundedness condition. This is crucial in proving
Prediction with incomplete past and interpolation of missing values
A generalized innovation algorithm is used to solve the problems of prediction of future values based on incomplete past and interpolation of missing values of a stationary time series. The emphasis
Duality of the weak parallelogram laws on Banach spaces
Abstract This paper explores a family of weak parallelogram laws for Banach spaces. Some basic properties of such spaces are obtained. The main result is that a Banach space satisfies a lower weak
On the geometry of Lp (μ) with applications to infinite variance processes
Abstract Some geometric properties of Lp spaces are studied which shed light on the prediction of infinite variance processes. In particular, a Pythagorean theorem for Lp is derived. Improved growth
Inner Functions in Reproducing Kernel Spaces
In Beurling’s approach to inner functions for the shift operator S on the Hardy space H2, a function f is inner when f ⊥ Snf for all \(n \geqslant 1\). Inspired by this approach, this paper develops
Mate choice and the evolutionary stability of a fixed threshold in a sequential search strategy
Conditions on cross-generational perturbations of the distribution of male phenotypes that allow for the evolutionary stability of an environmentally canalized threshold are determined.
Higher Cycle Operations and a Unipotent Torelli Theorem for Graphs
Let $\Gamma$ be a connected bridgeless graph and fix a vertex $v$ of $\Gamma$. We introduce a bilinear map $\int\colon \mathbf{Z}\pi_1(\Gamma,v) \times T\mathrm{H}_1(\Gamma,\mathbf{Z}) \to