Matches in SemOpenAlex for { <https://semopenalex.org/work/W2003490810> ?p ?o ?g. }
Showing items 1 to 75 of
75
with 100 items per page.
- W2003490810 endingPage "291" @default.
- W2003490810 startingPage "251" @default.
- W2003490810 abstract "Let {B H (u)} u ∈ℝ be a fractional Brownian motion (fBm) with index H∈(0, 1) and (B H ) be the closure in L 2(Ω) of the span Sp(B H ) of the increments of fBm B H . It is well-known that, when B H = B 1/2 is the usual Brownian motion (Bm), an element X∈ (B 1/2) can be characterized by a unique function f X ∈L 2(ℝ), in which case one writes X in an integral form as X = ∫ℝ f X (u)dB 1/2(u). From a different, though equivalent, perspective, the space L 2(ℝ) forms a class of integrands for the integral on the real line with respect to Bm B 1/2. In this work we explore whether a similar characterization of elements of (B H ) can be obtained when H∈ (0, 1/2) or H∈ (1/2, 1). Since it is natural to define the integral of an elementary function f = ∑ k =1 n f k 1 [uk,uk+1) by ∑ k =1 n f k (B H (u k +1) −B H (u k )), we want the spaces of integrands to contain elementary functions. These classes of integrands are inner product spaces. If the space of integrands is not complete, then it characterizes only a strict subset of (B H ). When 0<H<1/2, by using the moving average representation of fBm B H , we construct a complete space of integrands. When 1/2<H<1, however, an analogous construction leads to a space of integrands which is not complete. When 0<H<1/2 or 1/2<H<1, we also consider a number of other spaces of integrands. While smaller and henceincomplete, they form a natural choice and are convenient to workwith. We compare these spaces of integrands to the reproducing kernel Hilbert space of fBm." @default.
- W2003490810 created "2016-06-24" @default.
- W2003490810 creator A5004623767 @default.
- W2003490810 creator A5043998799 @default.
- W2003490810 date "2000-10-01" @default.
- W2003490810 modified "2023-10-11" @default.
- W2003490810 title "Integration questions related to fractional Brownian motion" @default.
- W2003490810 cites W2003427294 @default.
- W2003490810 cites W2020402888 @default.
- W2003490810 cites W2029774109 @default.
- W2003490810 cites W2045086852 @default.
- W2003490810 cites W2069786653 @default.
- W2003490810 cites W2147576019 @default.
- W2003490810 cites W2180071254 @default.
- W2003490810 cites W375903583 @default.
- W2003490810 doi "https://doi.org/10.1007/s440-000-8016-7" @default.
- W2003490810 hasPublicationYear "2000" @default.
- W2003490810 type Work @default.
- W2003490810 sameAs 2003490810 @default.
- W2003490810 citedByCount "348" @default.
- W2003490810 countsByYear W20034908102012 @default.
- W2003490810 countsByYear W20034908102013 @default.
- W2003490810 countsByYear W20034908102014 @default.
- W2003490810 countsByYear W20034908102015 @default.
- W2003490810 countsByYear W20034908102016 @default.
- W2003490810 countsByYear W20034908102017 @default.
- W2003490810 countsByYear W20034908102018 @default.
- W2003490810 countsByYear W20034908102019 @default.
- W2003490810 countsByYear W20034908102020 @default.
- W2003490810 countsByYear W20034908102021 @default.
- W2003490810 countsByYear W20034908102022 @default.
- W2003490810 countsByYear W20034908102023 @default.
- W2003490810 crossrefType "journal-article" @default.
- W2003490810 hasAuthorship W2003490810A5004623767 @default.
- W2003490810 hasAuthorship W2003490810A5043998799 @default.
- W2003490810 hasBestOaLocation W20034908101 @default.
- W2003490810 hasConcept C105795698 @default.
- W2003490810 hasConcept C108819105 @default.
- W2003490810 hasConcept C112401455 @default.
- W2003490810 hasConcept C114614502 @default.
- W2003490810 hasConcept C134306372 @default.
- W2003490810 hasConcept C138885662 @default.
- W2003490810 hasConcept C2778572836 @default.
- W2003490810 hasConcept C33923547 @default.
- W2003490810 hasConcept C41895202 @default.
- W2003490810 hasConceptScore W2003490810C105795698 @default.
- W2003490810 hasConceptScore W2003490810C108819105 @default.
- W2003490810 hasConceptScore W2003490810C112401455 @default.
- W2003490810 hasConceptScore W2003490810C114614502 @default.
- W2003490810 hasConceptScore W2003490810C134306372 @default.
- W2003490810 hasConceptScore W2003490810C138885662 @default.
- W2003490810 hasConceptScore W2003490810C2778572836 @default.
- W2003490810 hasConceptScore W2003490810C33923547 @default.
- W2003490810 hasConceptScore W2003490810C41895202 @default.
- W2003490810 hasIssue "2" @default.
- W2003490810 hasLocation W20034908101 @default.
- W2003490810 hasOpenAccess W2003490810 @default.
- W2003490810 hasPrimaryLocation W20034908101 @default.
- W2003490810 hasRelatedWork W1573173092 @default.
- W2003490810 hasRelatedWork W2165241701 @default.
- W2003490810 hasRelatedWork W2373202200 @default.
- W2003490810 hasRelatedWork W2753870633 @default.
- W2003490810 hasRelatedWork W2915158306 @default.
- W2003490810 hasRelatedWork W2950151750 @default.
- W2003490810 hasRelatedWork W2960646972 @default.
- W2003490810 hasRelatedWork W3021897514 @default.
- W2003490810 hasRelatedWork W3034439966 @default.
- W2003490810 hasRelatedWork W4321513530 @default.
- W2003490810 hasVolume "118" @default.
- W2003490810 isParatext "false" @default.
- W2003490810 isRetracted "false" @default.
- W2003490810 magId "2003490810" @default.
- W2003490810 workType "article" @default.