Matches in SemOpenAlex for { <https://semopenalex.org/work/W2396950417> ?p ?o ?g. }
Showing items 1 to 88 of
88
with 100 items per page.
- W2396950417 endingPage "1017" @default.
- W2396950417 startingPage "995" @default.
- W2396950417 abstract "The Bernoulli sieve is the infinite Karlin “balls-in-boxes” scheme with random probabilities of stick-breaking type. Assuming that the number of placed balls equals n, we prove several functional limit theorems (FLTs) in the Skorohod space D[0,1] endowed with the J1- or M1-topology for the number Kn∗(t) of boxes containing at most [nt] balls, t∈[0,1], and the random distribution function Kn∗(t)/Kn∗(1), as n→∞. The limit processes for Kn∗(t) are of the form (X(1)−X((1−t)−))t∈[0,1], where X is either a Brownian motion, a spectrally negative stable Lévy process, or an inverse stable subordinator. The small value probabilities for the stick-breaking factor determine which of the alternatives occurs. If the logarithm of this factor is integrable, the limit process for Kn∗(t)/Kn∗(1) is a Lévy bridge. Our approach relies upon two novel ingredients and particularly enables us to dispense with a Poissonization-de-Poissonization step which has been an essential component in all the previous studies of Kn∗(1). First, for any Karlin occupancy scheme with deterministic probabilities (pk)k≥1, we obtain an approximation, uniformly in t∈[0,1], of the number of boxes with at most [nt] balls by a counting function defined in terms of (pk)k≥1. Second, we prove several FLTs for the number of visits to the interval [0,nt] by a perturbed random walk, as n→∞. If the stick-breaking factor has a beta distribution with parameters θ>0 and 1, the process (Kn∗(t))t∈[0,1] has the same distribution as a similar process defined by the number of cycles of length at most [nt] in a θ-biased random permutation a.k.a. a Ewens permutation with parameter θ. As a consequence, our FLT with Brownian limit forms a generalization of a FLT obtained earlier in the context of Ewens permutations by DeLaurentis and Pittel (1985), Hansen (1990), Donnelly et al. (1991), and Arratia and Tavaré (1992)." @default.
- W2396950417 created "2016-06-24" @default.
- W2396950417 creator A5030507672 @default.
- W2396950417 creator A5051774277 @default.
- W2396950417 creator A5090566468 @default.
- W2396950417 date "2017-03-01" @default.
- W2396950417 modified "2023-10-14" @default.
- W2396950417 title "Functional limit theorems for the number of occupied boxes in the Bernoulli sieve" @default.
- W2396950417 cites W1978298011 @default.
- W2396950417 cites W1990871665 @default.
- W2396950417 cites W2005085536 @default.
- W2396950417 cites W2011889857 @default.
- W2396950417 cites W2022171458 @default.
- W2396950417 cites W2053390290 @default.
- W2396950417 cites W2055823445 @default.
- W2396950417 cites W2064905420 @default.
- W2396950417 cites W2096681789 @default.
- W2396950417 cites W2103268360 @default.
- W2396950417 cites W2109191002 @default.
- W2396950417 cites W2117706501 @default.
- W2396950417 cites W2126323192 @default.
- W2396950417 cites W2567984560 @default.
- W2396950417 cites W3098759601 @default.
- W2396950417 cites W3100298211 @default.
- W2396950417 doi "https://doi.org/10.1016/j.spa.2016.07.007" @default.
- W2396950417 hasPublicationYear "2017" @default.
- W2396950417 type Work @default.
- W2396950417 sameAs 2396950417 @default.
- W2396950417 citedByCount "22" @default.
- W2396950417 countsByYear W23969504172016 @default.
- W2396950417 countsByYear W23969504172017 @default.
- W2396950417 countsByYear W23969504172018 @default.
- W2396950417 countsByYear W23969504172020 @default.
- W2396950417 countsByYear W23969504172021 @default.
- W2396950417 countsByYear W23969504172022 @default.
- W2396950417 crossrefType "journal-article" @default.
- W2396950417 hasAuthorship W2396950417A5030507672 @default.
- W2396950417 hasAuthorship W2396950417A5051774277 @default.
- W2396950417 hasAuthorship W2396950417A5090566468 @default.
- W2396950417 hasBestOaLocation W23969504172 @default.
- W2396950417 hasConcept C105795698 @default.
- W2396950417 hasConcept C112401455 @default.
- W2396950417 hasConcept C114614502 @default.
- W2396950417 hasConcept C118615104 @default.
- W2396950417 hasConcept C121194460 @default.
- W2396950417 hasConcept C127413603 @default.
- W2396950417 hasConcept C134306372 @default.
- W2396950417 hasConcept C146978453 @default.
- W2396950417 hasConcept C151201525 @default.
- W2396950417 hasConcept C152361515 @default.
- W2396950417 hasConcept C2781362121 @default.
- W2396950417 hasConcept C33923547 @default.
- W2396950417 hasConceptScore W2396950417C105795698 @default.
- W2396950417 hasConceptScore W2396950417C112401455 @default.
- W2396950417 hasConceptScore W2396950417C114614502 @default.
- W2396950417 hasConceptScore W2396950417C118615104 @default.
- W2396950417 hasConceptScore W2396950417C121194460 @default.
- W2396950417 hasConceptScore W2396950417C127413603 @default.
- W2396950417 hasConceptScore W2396950417C134306372 @default.
- W2396950417 hasConceptScore W2396950417C146978453 @default.
- W2396950417 hasConceptScore W2396950417C151201525 @default.
- W2396950417 hasConceptScore W2396950417C152361515 @default.
- W2396950417 hasConceptScore W2396950417C2781362121 @default.
- W2396950417 hasConceptScore W2396950417C33923547 @default.
- W2396950417 hasFunder F4320308269 @default.
- W2396950417 hasFunder F4320320879 @default.
- W2396950417 hasIssue "3" @default.
- W2396950417 hasLocation W23969504171 @default.
- W2396950417 hasLocation W23969504172 @default.
- W2396950417 hasOpenAccess W2396950417 @default.
- W2396950417 hasPrimaryLocation W23969504171 @default.
- W2396950417 hasRelatedWork W1614582176 @default.
- W2396950417 hasRelatedWork W2010088121 @default.
- W2396950417 hasRelatedWork W2017306172 @default.
- W2396950417 hasRelatedWork W2073826067 @default.
- W2396950417 hasRelatedWork W2185474785 @default.
- W2396950417 hasRelatedWork W2524656256 @default.
- W2396950417 hasRelatedWork W2556300962 @default.
- W2396950417 hasRelatedWork W2623885049 @default.
- W2396950417 hasRelatedWork W4214482878 @default.
- W2396950417 hasRelatedWork W4299167113 @default.
- W2396950417 hasVolume "127" @default.
- W2396950417 isParatext "false" @default.
- W2396950417 isRetracted "false" @default.
- W2396950417 magId "2396950417" @default.
- W2396950417 workType "article" @default.