Matches in SemOpenAlex for { <https://semopenalex.org/work/W4287645465> ?p ?o ?g. }
Showing items 1 to 61 of
61
with 100 items per page.
- W4287645465 abstract "We suggest a novel approach to polynomial processes solely based on a polynomial action operator. With this approach, we can analyse such processes on general state spaces, going far beyond Banach spaces. Moreover, we can be very flexible in the definition of what polynomial means. We show that polynomial process universally means affine drift. Simple assumptions on the polynomial action operators lead to stronger characterisations on the polynomial class of processes. In our framework we do not need to specify polynomials explicitly but can work with a general sequence of graded vector spaces of functions on the state space. Elements of these graded vector spaces form the monomials by introducing a sequence of vector space complements. The basic tool of our analysis is the polynomial action operator, which is a semigroup of operators mapping conditional expected values of monomials acting on the polynomial process to monomials of the same or lower grade. Unlike the classical Euclidean case, the polynomial action operator may not form a finite-dimensional subspace after a finite iteration, a property we call locally finite. We study abstract polynomial processes under both algebraic and topological assumptions on the polynomial actions, and establish an affine drift structure. Moreover, we characterize the covariance structure under similar but slightly stronger conditions. A crucial part in our analysis is the use of the (algebraic or topological) dual of the monomials of grade one, which serves as a linearization of the state space of the polynomial process. Our general framework covers polynomial processes with values in Banach spaces recently studied by Cuchiero and Svaluto-Ferro." @default.
- W4287645465 created "2022-07-25" @default.
- W4287645465 creator A5008841359 @default.
- W4287645465 creator A5035790187 @default.
- W4287645465 creator A5044987464 @default.
- W4287645465 date "2020-10-06" @default.
- W4287645465 modified "2023-09-27" @default.
- W4287645465 title "Abstract polynomial processes" @default.
- W4287645465 doi "https://doi.org/10.48550/arxiv.2010.02483" @default.
- W4287645465 hasPublicationYear "2020" @default.
- W4287645465 type Work @default.
- W4287645465 citedByCount "0" @default.
- W4287645465 crossrefType "posted-content" @default.
- W4287645465 hasAuthorship W4287645465A5008841359 @default.
- W4287645465 hasAuthorship W4287645465A5035790187 @default.
- W4287645465 hasAuthorship W4287645465A5044987464 @default.
- W4287645465 hasBestOaLocation W42876454651 @default.
- W4287645465 hasConcept C101044782 @default.
- W4287645465 hasConcept C101525915 @default.
- W4287645465 hasConcept C11252640 @default.
- W4287645465 hasConcept C118615104 @default.
- W4287645465 hasConcept C126352355 @default.
- W4287645465 hasConcept C132954091 @default.
- W4287645465 hasConcept C134306372 @default.
- W4287645465 hasConcept C173110770 @default.
- W4287645465 hasConcept C202444582 @default.
- W4287645465 hasConcept C33923547 @default.
- W4287645465 hasConcept C45025165 @default.
- W4287645465 hasConcept C90119067 @default.
- W4287645465 hasConcept C92757383 @default.
- W4287645465 hasConcept C97395012 @default.
- W4287645465 hasConceptScore W4287645465C101044782 @default.
- W4287645465 hasConceptScore W4287645465C101525915 @default.
- W4287645465 hasConceptScore W4287645465C11252640 @default.
- W4287645465 hasConceptScore W4287645465C118615104 @default.
- W4287645465 hasConceptScore W4287645465C126352355 @default.
- W4287645465 hasConceptScore W4287645465C132954091 @default.
- W4287645465 hasConceptScore W4287645465C134306372 @default.
- W4287645465 hasConceptScore W4287645465C173110770 @default.
- W4287645465 hasConceptScore W4287645465C202444582 @default.
- W4287645465 hasConceptScore W4287645465C33923547 @default.
- W4287645465 hasConceptScore W4287645465C45025165 @default.
- W4287645465 hasConceptScore W4287645465C90119067 @default.
- W4287645465 hasConceptScore W4287645465C92757383 @default.
- W4287645465 hasConceptScore W4287645465C97395012 @default.
- W4287645465 hasLocation W42876454651 @default.
- W4287645465 hasOpenAccess W4287645465 @default.
- W4287645465 hasPrimaryLocation W42876454651 @default.
- W4287645465 hasRelatedWork W1543706171 @default.
- W4287645465 hasRelatedWork W1576380577 @default.
- W4287645465 hasRelatedWork W1973507931 @default.
- W4287645465 hasRelatedWork W2084988136 @default.
- W4287645465 hasRelatedWork W2140446896 @default.
- W4287645465 hasRelatedWork W3185830269 @default.
- W4287645465 hasRelatedWork W4287645465 @default.
- W4287645465 hasRelatedWork W4292770613 @default.
- W4287645465 hasRelatedWork W4321347226 @default.
- W4287645465 hasRelatedWork W103050704 @default.
- W4287645465 isParatext "false" @default.
- W4287645465 isRetracted "false" @default.
- W4287645465 workType "article" @default.