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dc.contributor.author | Lee, Wha-Suck![]() |
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dc.contributor.author | Le Roux, Christiaan![]() |
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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 |