Distributional properties of first jump times of CBI processes with jump sizes in given Borel sets Article Swipe

View

Barczy, Matyas , Palau Sandra , Xue Yao ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2512.04935

We derive an expression for the joint distribution function of the first jump times of a continuous state and continuous time branching process with immigration (CBI process) with jump sizes in given Borel sets having finite total Lévy measures, which is defined as the sum of the measures appearing in the branching and immigration mechanisms of the CBI process in question. Our result generalizes a corresponding result of He and Li (2016), who considered this problem in case of a single Borel set having finite total Lévy measure.

Related Topics

Mathematical Analysis

Concepts

Mathematics Jump Branching process Function (biology) Finite set Combinatorics Distribution (mathematics) Joint probability distribution Set (abstract data type) Applied mathematics Borel measure Lévy process Jump process Expression (computer science) State (computer science) Borel set Stochastic process Discrete mathematics Branching (polymer chemistry) Statistical physics Mathematical analysis

Metadata

Type: preprint
Landing Page: https://doi.org/10.48550/arxiv.2512.04935
OA Status: green
OpenAlex ID: https://openalex.org/W7108917846

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W7108917846

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.48550/arxiv.2512.04935

Digital Object Identifier
Title: Distributional properties of first jump times of CBI processes with jump sizes in given Borel sets

Work title
Type: preprint

OpenAlex work type
Publication year: 2025

Year of publication
Publication date: 2025-12-04

Full publication date if available
Authors: Barczy, Matyas, Palau Sandra, Xue Yao

List of authors in order
Landing page: https://doi.org/10.48550/arxiv.2512.04935

Publisher landing page
Open access: Yes

Whether a free full text is available
OA status: green

Open access status per OpenAlex
OA URL: https://doi.org/10.48550/arxiv.2512.04935

Direct OA link when available
Concepts: Mathematics, Jump, Branching process, Function (biology), Finite set, Combinatorics, Distribution (mathematics), Joint probability distribution, Set (abstract data type), Applied mathematics, Borel measure, Lévy process, Jump process, Expression (computer science), State (computer science), Borel set, Stochastic process, Discrete mathematics, Branching (polymer chemistry), Statistical physics, Mathematical analysis

Top concepts (fields/topics) attached by OpenAlex
Cited by: 0

Total citation count in OpenAlex

Full payload

id	https://openalex.org/W7108917846
doi	https://doi.org/10.48550/arxiv.2512.04935
ids.doi	https://doi.org/10.48550/arxiv.2512.04935
ids.openalex	https://openalex.org/W7108917846
fwci
type	preprint
title	Distributional properties of first jump times of CBI processes with jump sizes in given Borel sets
biblio.issue
biblio.volume
biblio.last_page
biblio.first_page
is_xpac	False
apc_list
apc_paid
concepts[0].id	https://openalex.org/C33923547
concepts[0].level	0
concepts[0].score	0.8155228495597839
concepts[0].wikidata	https://www.wikidata.org/wiki/Q395
concepts[0].display_name	Mathematics
concepts[1].id	https://openalex.org/C2780695682
concepts[1].level	2
concepts[1].score	0.7605946660041809
concepts[1].wikidata	https://www.wikidata.org/wiki/Q4005959
concepts[1].display_name	Jump
concepts[2].id	https://openalex.org/C177255742
concepts[2].level	2
concepts[2].score	0.46111053228378296
concepts[2].wikidata	https://www.wikidata.org/wiki/Q4109953
concepts[2].display_name	Branching process
concepts[3].id	https://openalex.org/C14036430
concepts[3].level	2
concepts[3].score	0.44279906153678894
concepts[3].wikidata	https://www.wikidata.org/wiki/Q3736076
concepts[3].display_name	Function (biology)
concepts[4].id	https://openalex.org/C162392398
concepts[4].level	2
concepts[4].score	0.4219243824481964
concepts[4].wikidata	https://www.wikidata.org/wiki/Q272404
concepts[4].display_name	Finite set
concepts[5].id	https://openalex.org/C114614502
concepts[5].level	1
concepts[5].score	0.38180622458457947
concepts[5].wikidata	https://www.wikidata.org/wiki/Q76592
concepts[5].display_name	Combinatorics
concepts[6].id	https://openalex.org/C110121322
concepts[6].level	2
concepts[6].score	0.36962756514549255
concepts[6].wikidata	https://www.wikidata.org/wiki/Q865811
concepts[6].display_name	Distribution (mathematics)
concepts[7].id	https://openalex.org/C18653775
concepts[7].level	2
concepts[7].score	0.3564392626285553
concepts[7].wikidata	https://www.wikidata.org/wiki/Q1333358
concepts[7].display_name	Joint probability distribution
concepts[8].id	https://openalex.org/C177264268
concepts[8].level	2
concepts[8].score	0.34591853618621826
concepts[8].wikidata	https://www.wikidata.org/wiki/Q1514741
concepts[8].display_name	Set (abstract data type)
concepts[9].id	https://openalex.org/C28826006
concepts[9].level	1
concepts[9].score	0.3398001492023468
concepts[9].wikidata	https://www.wikidata.org/wiki/Q33521
concepts[9].display_name	Applied mathematics
concepts[10].id	https://openalex.org/C166758865
concepts[10].level	3
concepts[10].score	0.3371858596801758
concepts[10].wikidata	https://www.wikidata.org/wiki/Q892585
concepts[10].display_name	Borel measure
concepts[11].id	https://openalex.org/C88757350
concepts[11].level	2
concepts[11].score	0.33645403385162354
concepts[11].wikidata	https://www.wikidata.org/wiki/Q1557613
concepts[11].display_name	Lévy process
concepts[12].id	https://openalex.org/C2776825372
concepts[12].level	3
concepts[12].score	0.3330066204071045
concepts[12].wikidata	https://www.wikidata.org/wiki/Q3922411
concepts[12].display_name	Jump process
concepts[13].id	https://openalex.org/C90559484
concepts[13].level	2
concepts[13].score	0.33254796266555786
concepts[13].wikidata	https://www.wikidata.org/wiki/Q778379
concepts[13].display_name	Expression (computer science)
concepts[14].id	https://openalex.org/C48103436
concepts[14].level	2
concepts[14].score	0.3268360495567322
concepts[14].wikidata	https://www.wikidata.org/wiki/Q599031
concepts[14].display_name	State (computer science)
concepts[15].id	https://openalex.org/C39952206
concepts[15].level	2
concepts[15].score	0.3226875066757202
concepts[15].wikidata	https://www.wikidata.org/wiki/Q21086747
concepts[15].display_name	Borel set
concepts[16].id	https://openalex.org/C8272713
concepts[16].level	2
concepts[16].score	0.3032247722148895
concepts[16].wikidata	https://www.wikidata.org/wiki/Q176737
concepts[16].display_name	Stochastic process
concepts[17].id	https://openalex.org/C118615104
concepts[17].level	1
concepts[17].score	0.28273797035217285
concepts[17].wikidata	https://www.wikidata.org/wiki/Q121416
concepts[17].display_name	Discrete mathematics
concepts[18].id	https://openalex.org/C206175624
concepts[18].level	2
concepts[18].score	0.2745628356933594
concepts[18].wikidata	https://www.wikidata.org/wiki/Q595731
concepts[18].display_name	Branching (polymer chemistry)
concepts[19].id	https://openalex.org/C121864883
concepts[19].level	1
concepts[19].score	0.26165828108787537
concepts[19].wikidata	https://www.wikidata.org/wiki/Q677916
concepts[19].display_name	Statistical physics
concepts[20].id	https://openalex.org/C134306372
concepts[20].level	1
concepts[20].score	0.25908276438713074
concepts[20].wikidata	https://www.wikidata.org/wiki/Q7754
concepts[20].display_name	Mathematical analysis
keywords[0].id	https://openalex.org/keywords/jump
keywords[0].score	0.7605946660041809
keywords[0].display_name	Jump
keywords[1].id	https://openalex.org/keywords/branching-process
keywords[1].score	0.46111053228378296
keywords[1].display_name	Branching process
keywords[2].id	https://openalex.org/keywords/function
keywords[2].score	0.44279906153678894
keywords[2].display_name	Function (biology)
keywords[3].id	https://openalex.org/keywords/finite-set
keywords[3].score	0.4219243824481964
keywords[3].display_name	Finite set
keywords[4].id	https://openalex.org/keywords/distribution
keywords[4].score	0.36962756514549255
keywords[4].display_name	Distribution (mathematics)
keywords[5].id	https://openalex.org/keywords/joint-probability-distribution
keywords[5].score	0.3564392626285553
keywords[5].display_name	Joint probability distribution
keywords[6].id	https://openalex.org/keywords/set
keywords[6].score	0.34591853618621826
keywords[6].display_name	Set (abstract data type)
language
locations[0].id	doi:10.48550/arxiv.2512.04935
locations[0].is_oa	True
locations[0].source.id	https://openalex.org/S4306400194
locations[0].source.issn
locations[0].source.type	repository
locations[0].source.is_oa	True
locations[0].source.issn_l
locations[0].source.is_core	False
locations[0].source.is_in_doaj	False
locations[0].source.display_name	arXiv (Cornell University)
locations[0].source.host_organization	https://openalex.org/I205783295
locations[0].source.host_organization_name	Cornell University
locations[0].source.host_organization_lineage	https://openalex.org/I205783295
locations[0].license
locations[0].pdf_url
locations[0].version
locations[0].raw_type	article
locations[0].license_id
locations[0].is_accepted	False
locations[0].is_published
locations[0].raw_source_name
locations[0].landing_page_url	https://doi.org/10.48550/arxiv.2512.04935
indexed_in	datacite
authorships[0].author.id	https://openalex.org/A4200892351
authorships[0].author.orcid
authorships[0].author.display_name	Barczy, Matyas
authorships[0].author_position	first
authorships[0].raw_author_name	Barczy, Matyas
authorships[0].is_corresponding	True
authorships[1].author.id	https://openalex.org/A4222474447
authorships[1].author.orcid
authorships[1].author.display_name	Palau Sandra
authorships[1].author_position	middle
authorships[1].raw_author_name	Palau, Sandra
authorships[1].is_corresponding	False
authorships[2].author.id	https://openalex.org/A2187972768
authorships[2].author.orcid	https://orcid.org/0000-0001-7360-2561
authorships[2].author.display_name	Xue Yao
authorships[2].author_position	last
authorships[2].raw_author_name	Xue, Yao
authorships[2].is_corresponding	False
has_content.pdf	False
has_content.grobid_xml	False
is_paratext	False
open_access.is_oa	True
open_access.oa_url	https://doi.org/10.48550/arxiv.2512.04935
open_access.oa_status	green
open_access.any_repository_has_fulltext	False
created_date	2025-12-06T00:00:00
display_name	Distributional properties of first jump times of CBI processes with jump sizes in given Borel sets
has_fulltext	False
is_retracted	False
updated_date	2025-12-06T23:14:57.273132
primary_topic
cited_by_count	0
locations_count	1
best_oa_location.id	doi:10.48550/arxiv.2512.04935
best_oa_location.is_oa	True
best_oa_location.source.id	https://openalex.org/S4306400194
best_oa_location.source.issn
best_oa_location.source.type	repository
best_oa_location.source.is_oa	True
best_oa_location.source.issn_l
best_oa_location.source.is_core	False
best_oa_location.source.is_in_doaj	False
best_oa_location.source.display_name	arXiv (Cornell University)
best_oa_location.source.host_organization	https://openalex.org/I205783295
best_oa_location.source.host_organization_name	Cornell University
best_oa_location.source.host_organization_lineage	https://openalex.org/I205783295
best_oa_location.license
best_oa_location.pdf_url
best_oa_location.version
best_oa_location.raw_type	article
best_oa_location.license_id
best_oa_location.is_accepted	False
best_oa_location.is_published	False
best_oa_location.raw_source_name
best_oa_location.landing_page_url	https://doi.org/10.48550/arxiv.2512.04935
primary_location.id	doi:10.48550/arxiv.2512.04935
primary_location.is_oa	True
primary_location.source.id	https://openalex.org/S4306400194
primary_location.source.issn
primary_location.source.type	repository
primary_location.source.is_oa	True
primary_location.source.issn_l
primary_location.source.is_core	False
primary_location.source.is_in_doaj	False
primary_location.source.display_name	arXiv (Cornell University)
primary_location.source.host_organization	https://openalex.org/I205783295
primary_location.source.host_organization_name	Cornell University
primary_location.source.host_organization_lineage	https://openalex.org/I205783295
primary_location.license
primary_location.pdf_url
primary_location.version
primary_location.raw_type	article
primary_location.license_id
primary_location.is_accepted	False
primary_location.is_published	False
primary_location.raw_source_name
primary_location.landing_page_url	https://doi.org/10.48550/arxiv.2512.04935
publication_date	2025-12-04
publication_year	2025
referenced_works_count	0
abstract_inverted_index.a	15, 64, 79
abstract_inverted_index.He	68
abstract_inverted_index.Li	70
abstract_inverted_index.We	0
abstract_inverted_index.an	2
abstract_inverted_index.as	42
abstract_inverted_index.in	30, 49, 59, 76
abstract_inverted_index.is	40
abstract_inverted_index.of	9, 14, 45, 55, 67, 78
abstract_inverted_index.CBI	57
abstract_inverted_index.Our	61
abstract_inverted_index.and	18, 52, 69
abstract_inverted_index.for	4
abstract_inverted_index.set	82
abstract_inverted_index.sum	44
abstract_inverted_index.the	5, 10, 43, 46, 50, 56
abstract_inverted_index.who	72
abstract_inverted_index.(CBI	25
abstract_inverted_index.case	77
abstract_inverted_index.jump	12, 28
abstract_inverted_index.sets	33
abstract_inverted_index.this	74
abstract_inverted_index.time	20
abstract_inverted_index.with	23, 27
abstract_inverted_index.Borel	32, 81
abstract_inverted_index.Lévy	37, 86
abstract_inverted_index.first	11
abstract_inverted_index.given	31
abstract_inverted_index.joint	6
abstract_inverted_index.sizes	29
abstract_inverted_index.state	17
abstract_inverted_index.times	13
abstract_inverted_index.total	36, 85
abstract_inverted_index.which	39
abstract_inverted_index.derive	1
abstract_inverted_index.finite	35, 84
abstract_inverted_index.having	34, 83
abstract_inverted_index.result	62, 66
abstract_inverted_index.single	80
abstract_inverted_index.(2016),	71
abstract_inverted_index.defined	41
abstract_inverted_index.problem	75
abstract_inverted_index.process	22, 58
abstract_inverted_index.function	8
abstract_inverted_index.measure.	87
abstract_inverted_index.measures	47
abstract_inverted_index.process)	26
abstract_inverted_index.appearing	48
abstract_inverted_index.branching	21, 51
abstract_inverted_index.measures,	38
abstract_inverted_index.question.	60
abstract_inverted_index.considered	73
abstract_inverted_index.continuous	16, 19
abstract_inverted_index.expression	3
abstract_inverted_index.mechanisms	54
abstract_inverted_index.generalizes	63
abstract_inverted_index.immigration	24, 53
abstract_inverted_index.distribution	7
abstract_inverted_index.corresponding	65
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	3
citation_normalized_percentile