The Asymptotic Behavior for Generalized Jiřina Process Article Swipe
You Lv
,
Huaping Huang
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.3390/axioms12010013
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.3390/axioms12010013
As the classic branching process, the Galton-Watson process has obtained intensive attentions in the past decades. However, this model has two idealized assumptions–discrete states and time-homogeneity. In the present paper, we consider a branching process with continuous states, and for any given n∈N, the branching law of every particle in generation n is determined by the population size of generation n. We consider the case that the process is extinct with Probability 1 since in this case the process will be substantially different from the size-dependent branching process with discrete states. We give the extinction rate in the sense of L2 and almost surely by the form of harmonic moments, that is to say, we show how fast {Zn−1} grows under a group of sufficient conditions. From the result of the present paper, we observe that the extinction rate will be determined by an asymptotic behavior of the mean of the branching law. The results obtained in this paper have the more superiority than the counterpart from the existing literature.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3390/axioms12010013
- https://www.mdpi.com/2075-1680/12/1/13/pdf?version=1673591319
- OA Status
- gold
- Cited By
- 1
- References
- 12
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4312172239
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Raw OpenAlex JSON
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https://openalex.org/W4312172239Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.3390/axioms12010013Digital Object Identifier
- Title
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The Asymptotic Behavior for Generalized Jiřina ProcessWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2022Year of publication
- Publication date
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2022-12-23Full publication date if available
- Authors
-
You Lv, Huaping HuangList of authors in order
- Landing page
-
https://doi.org/10.3390/axioms12010013Publisher landing page
- PDF URL
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https://www.mdpi.com/2075-1680/12/1/13/pdf?version=1673591319Direct link to full text PDF
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goldOpen access status per OpenAlex
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https://www.mdpi.com/2075-1680/12/1/13/pdf?version=1673591319Direct OA link when available
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Branching process, Mathematics, Branching (polymer chemistry), Statistical physics, Extinction (optical mineralogy), Extinction probability, Population, Applied mathematics, Population size, Combinatorics, Physics, Demography, Composite material, Optics, Sociology, Materials scienceTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
1Total citation count in OpenAlex
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2023: 1Per-year citation counts (last 5 years)
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12Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.give | 92 |
| abstract_inverted_index.have | 159 |
| abstract_inverted_index.law. | 152 |
| abstract_inverted_index.mean | 148 |
| abstract_inverted_index.more | 161 |
| abstract_inverted_index.past | 14 |
| abstract_inverted_index.rate | 95, 138 |
| abstract_inverted_index.say, | 113 |
| abstract_inverted_index.show | 115 |
| abstract_inverted_index.size | 57 |
| abstract_inverted_index.than | 163 |
| abstract_inverted_index.that | 65, 110, 135 |
| abstract_inverted_index.this | 17, 75, 157 |
| abstract_inverted_index.will | 79, 139 |
| abstract_inverted_index.with | 35, 70, 88 |
| abstract_inverted_index.every | 47 |
| abstract_inverted_index.given | 41 |
| abstract_inverted_index.group | 122 |
| abstract_inverted_index.grows | 119 |
| abstract_inverted_index.model | 18 |
| abstract_inverted_index.paper | 158 |
| abstract_inverted_index.sense | 98 |
| abstract_inverted_index.since | 73 |
| abstract_inverted_index.under | 120 |
| abstract_inverted_index.almost | 102 |
| abstract_inverted_index.n∈N, | 42 |
| abstract_inverted_index.paper, | 29, 132 |
| abstract_inverted_index.result | 128 |
| abstract_inverted_index.states | 23 |
| abstract_inverted_index.surely | 103 |
| abstract_inverted_index.classic | 2 |
| abstract_inverted_index.extinct | 69 |
| abstract_inverted_index.observe | 134 |
| abstract_inverted_index.present | 28, 131 |
| abstract_inverted_index.process | 7, 34, 67, 78, 87 |
| abstract_inverted_index.results | 154 |
| abstract_inverted_index.states, | 37 |
| abstract_inverted_index.states. | 90 |
| abstract_inverted_index.However, | 16 |
| abstract_inverted_index.behavior | 145 |
| abstract_inverted_index.consider | 31, 62 |
| abstract_inverted_index.decades. | 15 |
| abstract_inverted_index.discrete | 89 |
| abstract_inverted_index.existing | 168 |
| abstract_inverted_index.harmonic | 108 |
| abstract_inverted_index.moments, | 109 |
| abstract_inverted_index.obtained | 9, 155 |
| abstract_inverted_index.particle | 48 |
| abstract_inverted_index.process, | 4 |
| abstract_inverted_index.{Zn−1} | 118 |
| abstract_inverted_index.branching | 3, 33, 44, 86, 151 |
| abstract_inverted_index.different | 82 |
| abstract_inverted_index.idealized | 21 |
| abstract_inverted_index.intensive | 10 |
| abstract_inverted_index.asymptotic | 144 |
| abstract_inverted_index.attentions | 11 |
| abstract_inverted_index.continuous | 36 |
| abstract_inverted_index.determined | 53, 141 |
| abstract_inverted_index.extinction | 94, 137 |
| abstract_inverted_index.generation | 50, 59 |
| abstract_inverted_index.population | 56 |
| abstract_inverted_index.sufficient | 124 |
| abstract_inverted_index.Probability | 71 |
| abstract_inverted_index.conditions. | 125 |
| abstract_inverted_index.counterpart | 165 |
| abstract_inverted_index.literature. | 169 |
| abstract_inverted_index.superiority | 162 |
| abstract_inverted_index.Galton-Watson | 6 |
| abstract_inverted_index.substantially | 81 |
| abstract_inverted_index.size-dependent | 85 |
| abstract_inverted_index.time-homogeneity. | 25 |
| abstract_inverted_index.assumptions–discrete | 22 |
| cited_by_percentile_year.max | 94 |
| cited_by_percentile_year.min | 89 |
| corresponding_author_ids | https://openalex.org/A5082674305 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 2 |
| corresponding_institution_ids | https://openalex.org/I181326427 |
| citation_normalized_percentile.value | 0.60937096 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |