4 papers
Zeroes and Extrema of Functions via Random Measures
Athanasios Christou Micheas
We present methods that provide all zeroes and extrema of a function that do not require differentiation. Using point process theory, we are able to describe the locations of zeroe…
The Taylor Measure and its Applications
Athanasios Christou Micheas
We propose and study a novel collection of signed measures, which will be apply called Taylor measures. Stochastic versions of the new measures are also defined and studied. We ill…
Stochastic Taylor expansion via Poisson point processes
Weichao Wu, Athanasios C. Micheas
We generalize Taylor's theorem by introducing a stochastic formulation based on an underlying Poisson point process model. We utilize this approach to propose a novel non-linear re…
The Multivariate Taylor Measure Function Space and a Generalization of Taylor's Theorem
Athanasios Christou Micheas
Using the recently defined concept of Taylor measures, we propose a generalization of Taylor's theorem to measurable, non-analytic functions, that do not require differentiation. W…