Convolution algebra for extended Feller convolution
Abstract
We apply the recently introduced framework of admissible homomorphisms in the form of a convolution algebra of C2-valued admissible homomorphisms to handle two-dimensional uni-directional homogeneous stochastic kernels. The algebra product is a non-commutative extension of the Feller convolution needed for an adequate operator representation of such kernels: a pair of homogeneous transition functions uni-directionally intertwined by the extended Chapman–Kolmogorov equation is a convolution empathy; the associated Fokker–Planck equations are re-written as an implicit Cauchy equation expressed in terms of admissible homomorphisms. The conditions of solvability of such implicit evolution equations follow from the consideration of generators of a convolution empathy
URI
http://hdl.handle.net/10394/36516https://link.springer.com/article/10.1007/s00233-020-10145-y
https://doi.org/10.1007/s00233-020-10145-y
Collections
Related items
Showing items related by title, author, creator and subject.
-
Source classification in deep radio surveys using machine learning techniques
Hosenie, Zafiirah Banon (North-West University, 2018)Until now radio galaxies have primarily been classified using the human neural system. The Square Kilometre Array (SKA) will, however, produce a very large amount of science data, extending into the multiple-petabyte range. ... -
Stride and translation invariance in CNNs
Mouton, Coenraad; Myburgh, Johannes C.; Davel, Marelie H. (Southern African Conference for Artificial Intelligence Research, 2020)Convolutional Neural Networks have become the standard for image classification tasks, however, these architectures are not invariant to translations of the input image. This lack of invariance is attributed to the use of ... -
Tracking translation invariance in CNNs
Myburgh, Johannes C.; Mouton, Coenraad; Davel, Marelie H. (Southern African Conference for Artificial Intelligence Research, 2020)Although Convolutional Neural Networks (CNNs) are widely used, their translation invariance (ability to deal with translated inputs) is still subject to some controversy. We explore this question using translation-sensitivity ...