Convolution algebra for extended Feller convolution

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dc.contributor.author Lee, Wha-Suck
dc.contributor.author Le Roux, Christiaan
dc.date.accessioned 2021-04-19T07:37:01Z
dc.date.issued 2021-02
dc.description.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. en_ZA
dc.description.department Mathematics and Applied Mathematics en_ZA
dc.description.embargo 2021-12-01
dc.description.librarian hj2021 en_ZA
dc.description.sponsorship Claude Leon Foundation and the NWU Postoctoral Fellowship. en_ZA
dc.description.uri http://link.springer.com/journal/233 en_ZA
dc.identifier.citation Lee, WS., Le Roux, C. Convolution algebra for extended Feller convolution. Semigroup Forum 102, 184–216 (2021). https://doi.org/10.1007/s00233-020-10145-y. en_ZA
dc.identifier.issn 0037-1912 (print)
dc.identifier.issn 1432-2137 (online)
dc.identifier.other 10.1007/s00233-020-10145-y
dc.identifier.uri http://hdl.handle.net/2263/79492
dc.language.iso en en_ZA
dc.publisher Springer en_ZA
dc.rights © 2020, Springer Science Business Media, LLC, part of Springer Nature. The original publication is available at http://link.springer.com/journal/233. en_ZA
dc.subject Convolution empathy en_ZA
dc.subject Feller convolution en_ZA
dc.subject Extended Chapman–Kolmogorov equation en_ZA
dc.subject Intertwined homogeneous Markov processes en_ZA
dc.subject Implicit Fokker–Planck equations en_ZA
dc.subject Admissible homomorphisms en_ZA
dc.subject Convolution algebra en_ZA
dc.subject Two-dimensional uni-directional stochastic kernel en_ZA
dc.title Convolution algebra for extended Feller convolution en_ZA
dc.type Postprint Article en_ZA


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