A Phase Transition for Large Values of Bifurcating Autoregressive Models
Abstract We describe the asymptotic behavior of the number $$Z_n[a_n,\infty )$$ of individuals with a large value in a stable bifurcating autoregressive process, where $$a_n\rightarrow \infty $$. The study of the associated first moment is equivalent to the annealed large deviation problem of an aut...
Ausführliche Beschreibung
Gespeichert in:
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Bansaye, Vincent [verfasserIn] |
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Artikel |
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Englisch |
| Erschienen: |
2020 |
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| Anmerkung: |
© Springer Science+Business Media, LLC, part of Springer Nature 2020 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of theoretical probability - Springer US, 1988, 34(2020), 4 vom: 28. Aug., Seite 2081-2116 |
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| Übergeordnetes Werk: |
volume:34 ; year:2020 ; number:4 ; day:28 ; month:08 ; pages:2081-2116 |
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10.1007/s10959-020-01033-w |
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| 520 | |a Abstract We describe the asymptotic behavior of the number $$Z_n[a_n,\infty )$$ of individuals with a large value in a stable bifurcating autoregressive process, where $$a_n\rightarrow \infty $$. The study of the associated first moment is equivalent to the annealed large deviation problem of an autoregressive process in a random environment. The trajectorial behavior of $$Z_n[a_n,\infty )$$ is obtained by the study of the ancestral paths corresponding to the large deviation event together with the environment of the process. This study of large deviations of autoregressive processes in random environment is of independent interest and achieved first. The estimates for bifurcating autoregressive process involve then a law of large numbers for non-homogenous trees. Two regimes appear in the stable case, depending on whether one of the autoregressive parameters is greater than 1 or not. It yields different asymptotic behaviors for large local densities and maximal value of the bifurcating autoregressive process. | ||
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10.1007/s10959-020-01033-w doi (DE-627)OLC2077229586 (DE-He213)s10959-020-01033-w-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Bansaye, Vincent verfasserin aut A Phase Transition for Large Values of Bifurcating Autoregressive Models 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract We describe the asymptotic behavior of the number $$Z_n[a_n,\infty )$$ of individuals with a large value in a stable bifurcating autoregressive process, where $$a_n\rightarrow \infty $$. The study of the associated first moment is equivalent to the annealed large deviation problem of an autoregressive process in a random environment. The trajectorial behavior of $$Z_n[a_n,\infty )$$ is obtained by the study of the ancestral paths corresponding to the large deviation event together with the environment of the process. This study of large deviations of autoregressive processes in random environment is of independent interest and achieved first. The estimates for bifurcating autoregressive process involve then a law of large numbers for non-homogenous trees. Two regimes appear in the stable case, depending on whether one of the autoregressive parameters is greater than 1 or not. It yields different asymptotic behaviors for large local densities and maximal value of the bifurcating autoregressive process. Branching process Autoregressive process Random environment Large deviations Bitseki Penda, S. Valère (orcid)0000-0001-8728-1586 aut Enthalten in Journal of theoretical probability Springer US, 1988 34(2020), 4 vom: 28. Aug., Seite 2081-2116 (DE-627)129930903 (DE-600)357043-5 (DE-576)018191886 0894-9840 nnns volume:34 year:2020 number:4 day:28 month:08 pages:2081-2116 https://doi.org/10.1007/s10959-020-01033-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4027 AR 34 2020 4 28 08 2081-2116 |
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10.1007/s10959-020-01033-w doi (DE-627)OLC2077229586 (DE-He213)s10959-020-01033-w-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Bansaye, Vincent verfasserin aut A Phase Transition for Large Values of Bifurcating Autoregressive Models 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract We describe the asymptotic behavior of the number $$Z_n[a_n,\infty )$$ of individuals with a large value in a stable bifurcating autoregressive process, where $$a_n\rightarrow \infty $$. The study of the associated first moment is equivalent to the annealed large deviation problem of an autoregressive process in a random environment. The trajectorial behavior of $$Z_n[a_n,\infty )$$ is obtained by the study of the ancestral paths corresponding to the large deviation event together with the environment of the process. This study of large deviations of autoregressive processes in random environment is of independent interest and achieved first. The estimates for bifurcating autoregressive process involve then a law of large numbers for non-homogenous trees. Two regimes appear in the stable case, depending on whether one of the autoregressive parameters is greater than 1 or not. It yields different asymptotic behaviors for large local densities and maximal value of the bifurcating autoregressive process. Branching process Autoregressive process Random environment Large deviations Bitseki Penda, S. Valère (orcid)0000-0001-8728-1586 aut Enthalten in Journal of theoretical probability Springer US, 1988 34(2020), 4 vom: 28. Aug., Seite 2081-2116 (DE-627)129930903 (DE-600)357043-5 (DE-576)018191886 0894-9840 nnns volume:34 year:2020 number:4 day:28 month:08 pages:2081-2116 https://doi.org/10.1007/s10959-020-01033-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4027 AR 34 2020 4 28 08 2081-2116 |
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10.1007/s10959-020-01033-w doi (DE-627)OLC2077229586 (DE-He213)s10959-020-01033-w-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Bansaye, Vincent verfasserin aut A Phase Transition for Large Values of Bifurcating Autoregressive Models 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract We describe the asymptotic behavior of the number $$Z_n[a_n,\infty )$$ of individuals with a large value in a stable bifurcating autoregressive process, where $$a_n\rightarrow \infty $$. The study of the associated first moment is equivalent to the annealed large deviation problem of an autoregressive process in a random environment. The trajectorial behavior of $$Z_n[a_n,\infty )$$ is obtained by the study of the ancestral paths corresponding to the large deviation event together with the environment of the process. This study of large deviations of autoregressive processes in random environment is of independent interest and achieved first. The estimates for bifurcating autoregressive process involve then a law of large numbers for non-homogenous trees. Two regimes appear in the stable case, depending on whether one of the autoregressive parameters is greater than 1 or not. It yields different asymptotic behaviors for large local densities and maximal value of the bifurcating autoregressive process. Branching process Autoregressive process Random environment Large deviations Bitseki Penda, S. Valère (orcid)0000-0001-8728-1586 aut Enthalten in Journal of theoretical probability Springer US, 1988 34(2020), 4 vom: 28. Aug., Seite 2081-2116 (DE-627)129930903 (DE-600)357043-5 (DE-576)018191886 0894-9840 nnns volume:34 year:2020 number:4 day:28 month:08 pages:2081-2116 https://doi.org/10.1007/s10959-020-01033-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4027 AR 34 2020 4 28 08 2081-2116 |
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10.1007/s10959-020-01033-w doi (DE-627)OLC2077229586 (DE-He213)s10959-020-01033-w-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Bansaye, Vincent verfasserin aut A Phase Transition for Large Values of Bifurcating Autoregressive Models 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract We describe the asymptotic behavior of the number $$Z_n[a_n,\infty )$$ of individuals with a large value in a stable bifurcating autoregressive process, where $$a_n\rightarrow \infty $$. The study of the associated first moment is equivalent to the annealed large deviation problem of an autoregressive process in a random environment. The trajectorial behavior of $$Z_n[a_n,\infty )$$ is obtained by the study of the ancestral paths corresponding to the large deviation event together with the environment of the process. This study of large deviations of autoregressive processes in random environment is of independent interest and achieved first. The estimates for bifurcating autoregressive process involve then a law of large numbers for non-homogenous trees. Two regimes appear in the stable case, depending on whether one of the autoregressive parameters is greater than 1 or not. It yields different asymptotic behaviors for large local densities and maximal value of the bifurcating autoregressive process. Branching process Autoregressive process Random environment Large deviations Bitseki Penda, S. Valère (orcid)0000-0001-8728-1586 aut Enthalten in Journal of theoretical probability Springer US, 1988 34(2020), 4 vom: 28. Aug., Seite 2081-2116 (DE-627)129930903 (DE-600)357043-5 (DE-576)018191886 0894-9840 nnns volume:34 year:2020 number:4 day:28 month:08 pages:2081-2116 https://doi.org/10.1007/s10959-020-01033-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4027 AR 34 2020 4 28 08 2081-2116 |
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10.1007/s10959-020-01033-w doi (DE-627)OLC2077229586 (DE-He213)s10959-020-01033-w-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Bansaye, Vincent verfasserin aut A Phase Transition for Large Values of Bifurcating Autoregressive Models 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract We describe the asymptotic behavior of the number $$Z_n[a_n,\infty )$$ of individuals with a large value in a stable bifurcating autoregressive process, where $$a_n\rightarrow \infty $$. The study of the associated first moment is equivalent to the annealed large deviation problem of an autoregressive process in a random environment. The trajectorial behavior of $$Z_n[a_n,\infty )$$ is obtained by the study of the ancestral paths corresponding to the large deviation event together with the environment of the process. This study of large deviations of autoregressive processes in random environment is of independent interest and achieved first. The estimates for bifurcating autoregressive process involve then a law of large numbers for non-homogenous trees. Two regimes appear in the stable case, depending on whether one of the autoregressive parameters is greater than 1 or not. It yields different asymptotic behaviors for large local densities and maximal value of the bifurcating autoregressive process. Branching process Autoregressive process Random environment Large deviations Bitseki Penda, S. Valère (orcid)0000-0001-8728-1586 aut Enthalten in Journal of theoretical probability Springer US, 1988 34(2020), 4 vom: 28. Aug., Seite 2081-2116 (DE-627)129930903 (DE-600)357043-5 (DE-576)018191886 0894-9840 nnns volume:34 year:2020 number:4 day:28 month:08 pages:2081-2116 https://doi.org/10.1007/s10959-020-01033-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4027 AR 34 2020 4 28 08 2081-2116 |
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Abstract We describe the asymptotic behavior of the number $$Z_n[a_n,\infty )$$ of individuals with a large value in a stable bifurcating autoregressive process, where $$a_n\rightarrow \infty $$. The study of the associated first moment is equivalent to the annealed large deviation problem of an autoregressive process in a random environment. The trajectorial behavior of $$Z_n[a_n,\infty )$$ is obtained by the study of the ancestral paths corresponding to the large deviation event together with the environment of the process. This study of large deviations of autoregressive processes in random environment is of independent interest and achieved first. The estimates for bifurcating autoregressive process involve then a law of large numbers for non-homogenous trees. Two regimes appear in the stable case, depending on whether one of the autoregressive parameters is greater than 1 or not. It yields different asymptotic behaviors for large local densities and maximal value of the bifurcating autoregressive process. © Springer Science+Business Media, LLC, part of Springer Nature 2020 |
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Abstract We describe the asymptotic behavior of the number $$Z_n[a_n,\infty )$$ of individuals with a large value in a stable bifurcating autoregressive process, where $$a_n\rightarrow \infty $$. The study of the associated first moment is equivalent to the annealed large deviation problem of an autoregressive process in a random environment. The trajectorial behavior of $$Z_n[a_n,\infty )$$ is obtained by the study of the ancestral paths corresponding to the large deviation event together with the environment of the process. This study of large deviations of autoregressive processes in random environment is of independent interest and achieved first. The estimates for bifurcating autoregressive process involve then a law of large numbers for non-homogenous trees. Two regimes appear in the stable case, depending on whether one of the autoregressive parameters is greater than 1 or not. It yields different asymptotic behaviors for large local densities and maximal value of the bifurcating autoregressive process. © Springer Science+Business Media, LLC, part of Springer Nature 2020 |
| abstract_unstemmed |
Abstract We describe the asymptotic behavior of the number $$Z_n[a_n,\infty )$$ of individuals with a large value in a stable bifurcating autoregressive process, where $$a_n\rightarrow \infty $$. The study of the associated first moment is equivalent to the annealed large deviation problem of an autoregressive process in a random environment. The trajectorial behavior of $$Z_n[a_n,\infty )$$ is obtained by the study of the ancestral paths corresponding to the large deviation event together with the environment of the process. This study of large deviations of autoregressive processes in random environment is of independent interest and achieved first. The estimates for bifurcating autoregressive process involve then a law of large numbers for non-homogenous trees. Two regimes appear in the stable case, depending on whether one of the autoregressive parameters is greater than 1 or not. It yields different asymptotic behaviors for large local densities and maximal value of the bifurcating autoregressive process. © Springer Science+Business Media, LLC, part of Springer Nature 2020 |
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| title_short |
A Phase Transition for Large Values of Bifurcating Autoregressive Models |
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https://doi.org/10.1007/s10959-020-01033-w |
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Bitseki Penda, S. Valère |
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Bitseki Penda, S. Valère |
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| doi_str |
10.1007/s10959-020-01033-w |
| up_date |
2024-07-03T14:27:51.407Z |
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