Matches in SemOpenAlex for { <https://semopenalex.org/work/W4285037423> ?p ?o ?g. }
Showing items 1 to 54 of
54
with 100 items per page.
- W4285037423 abstract "Motivated by seminal paper of Kozlov et al.(1975) we consider in this paper a branching process with a geometric offspring distribution parametrized by random success probability $A$ and immigration equals $1$ in each generation. In contrast to above mentioned article, we assume that environment is heavy-tailed, that is $log A^{-1} (1-A)$ is regularly varying with a parameter $alpha>1$, that is that ${bf P} Big( log A^{-1} (1-A) > x Big) = x^{-alpha} L(x)$ for a slowly varying function $L$. We will prove that although the offspring distribution is light-tailed, the environment itself can produce extremely heavy tails of distribution of the population at $n$-th generation which gets even heavier with $n$ increasing. Precisely, in this work, we prove that asymptotic tail ${bf P}(Z_l ge m)$ of $l$-th population $Z_l$ is of order $ Big(log^{(l)} m Big)^{-alpha} L Big(log^{(l)} m Big)$ for large $m$, where $log^{(l)} m = log ldots log m$. The proof is mainly based on Tauberian theorem. Using this result we also analyze the asymptotic behaviour of the first passage time $T_n$ of the state $n in mathbb{Z}$ by the walker in a neighborhood random walk in random environment created by independent copies $(A_i : i in mathbb{Z})$ of $(0,1)$-valued random variable $A$. This version differs from the final version as it contains an alternative proof for the tail behavior for generation sizes which is not very sharp (lacks constant) but completely avoids arguments based on Tauberian theorem. This proof may be of an independent interest." @default.
- W4285037423 created "2022-07-12" @default.
- W4285037423 creator A5042364539 @default.
- W4285037423 creator A5044709164 @default.
- W4285037423 date "2019-06-25" @default.
- W4285037423 modified "2023-10-14" @default.
- W4285037423 title "Slower variation of the generation sizes induced by heavy-tailed environment for geometric branching" @default.
- W4285037423 doi "https://doi.org/10.48550/arxiv.1906.10498" @default.
- W4285037423 hasPublicationYear "2019" @default.
- W4285037423 type Work @default.
- W4285037423 citedByCount "0" @default.
- W4285037423 crossrefType "posted-content" @default.
- W4285037423 hasAuthorship W4285037423A5042364539 @default.
- W4285037423 hasAuthorship W4285037423A5044709164 @default.
- W4285037423 hasBestOaLocation W42850374231 @default.
- W4285037423 hasConcept C105795698 @default.
- W4285037423 hasConcept C110121322 @default.
- W4285037423 hasConcept C114614502 @default.
- W4285037423 hasConcept C121194460 @default.
- W4285037423 hasConcept C121332964 @default.
- W4285037423 hasConcept C134306372 @default.
- W4285037423 hasConcept C144024400 @default.
- W4285037423 hasConcept C149923435 @default.
- W4285037423 hasConcept C177255742 @default.
- W4285037423 hasConcept C2908647359 @default.
- W4285037423 hasConcept C33923547 @default.
- W4285037423 hasConceptScore W4285037423C105795698 @default.
- W4285037423 hasConceptScore W4285037423C110121322 @default.
- W4285037423 hasConceptScore W4285037423C114614502 @default.
- W4285037423 hasConceptScore W4285037423C121194460 @default.
- W4285037423 hasConceptScore W4285037423C121332964 @default.
- W4285037423 hasConceptScore W4285037423C134306372 @default.
- W4285037423 hasConceptScore W4285037423C144024400 @default.
- W4285037423 hasConceptScore W4285037423C149923435 @default.
- W4285037423 hasConceptScore W4285037423C177255742 @default.
- W4285037423 hasConceptScore W4285037423C2908647359 @default.
- W4285037423 hasConceptScore W4285037423C33923547 @default.
- W4285037423 hasLocation W42850374231 @default.
- W4285037423 hasLocation W42850374232 @default.
- W4285037423 hasOpenAccess W4285037423 @default.
- W4285037423 hasPrimaryLocation W42850374231 @default.
- W4285037423 hasRelatedWork W1978042415 @default.
- W4285037423 hasRelatedWork W1984953408 @default.
- W4285037423 hasRelatedWork W2017331178 @default.
- W4285037423 hasRelatedWork W2041338657 @default.
- W4285037423 hasRelatedWork W2165413682 @default.
- W4285037423 hasRelatedWork W2224314243 @default.
- W4285037423 hasRelatedWork W2260035625 @default.
- W4285037423 hasRelatedWork W2976797620 @default.
- W4285037423 hasRelatedWork W3086542228 @default.
- W4285037423 hasRelatedWork W3178083752 @default.
- W4285037423 isParatext "false" @default.
- W4285037423 isRetracted "false" @default.
- W4285037423 workType "article" @default.