Nonnegative idempotent kernels

Nonnegativity of Schur complements of nonnegative idempotent matrices

Let A be a nonnegative idempotent matrix. It is shown that the Schur complement of a submatrix, using the Moore-Penrose inverse, is a nonnegative idempotent matrix if the submatrix has a positive diagonal. Similar results for the Schur complement of any submatrix of A are no longer true in general.

Nonnegative Feynman-Kac Kernels in Schrödinger’s Interpolation Problem

The existing formulations of the Schrödinger interpolating dynamics, which is constrained by the prescribed input-output statistics data, utilize strictly positive Feynman-Kac kernels. This implies that the related Markov diffusion processes admit vanishing probability densities only at the boundaries of the spatial volume confining the process. We extend the framework to encompass singular pot...

Nonnegative bias reduction methods for density estimation using asymmetric kernels

Two classes of multiplicative bias correction (‘‘MBC’’) methods are applied to density estimation with support on [0, ∞). It is demonstrated that under sufficient smoothness of the true density, each MBC technique reduces the order of magnitude in bias, whereas the order of magnitude in variance remains unchanged. Accordingly, the mean integrated squared error of each MBC estimator achieves a f...

Idempotent Analogue of Resolvent Kernels for a Deterministic Optimal Control Problem

The Idempotent Analog of Resolvent Kernels for a Deterministic Optimal Control Problem

A solution of a discrete Hamilton–Jacobi–Bellman equation is represented in terms of idempotent analysis as a convergent series of integral operators.