Limiting distribution of sums of nonnegative stationary random variables
Summary Let {Xn,j,−∞<j<∞∼,n≧1, be a sequence of stationary sequences on some probability space, with nonnegative random variables. Under appropriate mixing conditions, it is shown thatSn=$ X_{n,1} $+…+Xn,n has a limiting distribution of a general infinitely divisible form. The result is applie...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Berman, Simeon M. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1984 |
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| Anmerkung: |
© The Institute of Statistical Mathematics, Tokyo 1984 |
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| Übergeordnetes Werk: |
Enthalten in: Annals of the Institute of Statistical Mathematics - Kluwer Academic Publishers-Plenum Publishers, 1949, 36(1984), 2 vom: 01. Dez., Seite 301-321 |
|---|---|
| Übergeordnetes Werk: |
volume:36 ; year:1984 ; number:2 ; day:01 ; month:12 ; pages:301-321 |
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| DOI / URN: |
10.1007/BF02481972 |
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| 520 | |a Summary Let {Xn,j,−∞<j<∞∼,n≧1, be a sequence of stationary sequences on some probability space, with nonnegative random variables. Under appropriate mixing conditions, it is shown thatSn=$ X_{n,1} $+…+Xn,n has a limiting distribution of a general infinitely divisible form. The result is applied to sequences of functions {fn(x)∼ defined on a stationary sequence {Xj∼, whereXn.f=$ f_{n} $($ X_{j} $). The results are illustrated by applications to Gaussian processes, Markov processes and some autoregressive processes of a general type. | ||
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10.1007/BF02481972 doi (DE-627)OLC2071677382 (DE-He213)BF02481972-p DE-627 ger DE-627 rakwb eng 510 VZ Berman, Simeon M. verfasserin aut Limiting distribution of sums of nonnegative stationary random variables 1984 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Institute of Statistical Mathematics, Tokyo 1984 Summary Let {Xn,j,−∞<j<∞∼,n≧1, be a sequence of stationary sequences on some probability space, with nonnegative random variables. Under appropriate mixing conditions, it is shown thatSn=$ X_{n,1} $+…+Xn,n has a limiting distribution of a general infinitely divisible form. The result is applied to sequences of functions {fn(x)∼ defined on a stationary sequence {Xj∼, whereXn.f=$ f_{n} $($ X_{j} $). The results are illustrated by applications to Gaussian processes, Markov processes and some autoregressive processes of a general type. Enthalten in Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers-Plenum Publishers, 1949 36(1984), 2 vom: 01. Dez., Seite 301-321 (DE-627)129934658 (DE-600)390313-8 (DE-576)015492907 0020-3157 nnns volume:36 year:1984 number:2 day:01 month:12 pages:301-321 https://doi.org/10.1007/BF02481972 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2012 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4316 GBV_ILN_4323 GBV_ILN_4324 AR 36 1984 2 01 12 301-321 |
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10.1007/BF02481972 doi (DE-627)OLC2071677382 (DE-He213)BF02481972-p DE-627 ger DE-627 rakwb eng 510 VZ Berman, Simeon M. verfasserin aut Limiting distribution of sums of nonnegative stationary random variables 1984 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Institute of Statistical Mathematics, Tokyo 1984 Summary Let {Xn,j,−∞<j<∞∼,n≧1, be a sequence of stationary sequences on some probability space, with nonnegative random variables. Under appropriate mixing conditions, it is shown thatSn=$ X_{n,1} $+…+Xn,n has a limiting distribution of a general infinitely divisible form. The result is applied to sequences of functions {fn(x)∼ defined on a stationary sequence {Xj∼, whereXn.f=$ f_{n} $($ X_{j} $). The results are illustrated by applications to Gaussian processes, Markov processes and some autoregressive processes of a general type. Enthalten in Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers-Plenum Publishers, 1949 36(1984), 2 vom: 01. Dez., Seite 301-321 (DE-627)129934658 (DE-600)390313-8 (DE-576)015492907 0020-3157 nnns volume:36 year:1984 number:2 day:01 month:12 pages:301-321 https://doi.org/10.1007/BF02481972 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2012 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4316 GBV_ILN_4323 GBV_ILN_4324 AR 36 1984 2 01 12 301-321 |
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10.1007/BF02481972 doi (DE-627)OLC2071677382 (DE-He213)BF02481972-p DE-627 ger DE-627 rakwb eng 510 VZ Berman, Simeon M. verfasserin aut Limiting distribution of sums of nonnegative stationary random variables 1984 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Institute of Statistical Mathematics, Tokyo 1984 Summary Let {Xn,j,−∞<j<∞∼,n≧1, be a sequence of stationary sequences on some probability space, with nonnegative random variables. Under appropriate mixing conditions, it is shown thatSn=$ X_{n,1} $+…+Xn,n has a limiting distribution of a general infinitely divisible form. The result is applied to sequences of functions {fn(x)∼ defined on a stationary sequence {Xj∼, whereXn.f=$ f_{n} $($ X_{j} $). The results are illustrated by applications to Gaussian processes, Markov processes and some autoregressive processes of a general type. Enthalten in Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers-Plenum Publishers, 1949 36(1984), 2 vom: 01. Dez., Seite 301-321 (DE-627)129934658 (DE-600)390313-8 (DE-576)015492907 0020-3157 nnns volume:36 year:1984 number:2 day:01 month:12 pages:301-321 https://doi.org/10.1007/BF02481972 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2012 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4316 GBV_ILN_4323 GBV_ILN_4324 AR 36 1984 2 01 12 301-321 |
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10.1007/BF02481972 doi (DE-627)OLC2071677382 (DE-He213)BF02481972-p DE-627 ger DE-627 rakwb eng 510 VZ Berman, Simeon M. verfasserin aut Limiting distribution of sums of nonnegative stationary random variables 1984 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Institute of Statistical Mathematics, Tokyo 1984 Summary Let {Xn,j,−∞<j<∞∼,n≧1, be a sequence of stationary sequences on some probability space, with nonnegative random variables. Under appropriate mixing conditions, it is shown thatSn=$ X_{n,1} $+…+Xn,n has a limiting distribution of a general infinitely divisible form. The result is applied to sequences of functions {fn(x)∼ defined on a stationary sequence {Xj∼, whereXn.f=$ f_{n} $($ X_{j} $). The results are illustrated by applications to Gaussian processes, Markov processes and some autoregressive processes of a general type. Enthalten in Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers-Plenum Publishers, 1949 36(1984), 2 vom: 01. Dez., Seite 301-321 (DE-627)129934658 (DE-600)390313-8 (DE-576)015492907 0020-3157 nnns volume:36 year:1984 number:2 day:01 month:12 pages:301-321 https://doi.org/10.1007/BF02481972 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2012 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4316 GBV_ILN_4323 GBV_ILN_4324 AR 36 1984 2 01 12 301-321 |
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10.1007/BF02481972 doi (DE-627)OLC2071677382 (DE-He213)BF02481972-p DE-627 ger DE-627 rakwb eng 510 VZ Berman, Simeon M. verfasserin aut Limiting distribution of sums of nonnegative stationary random variables 1984 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Institute of Statistical Mathematics, Tokyo 1984 Summary Let {Xn,j,−∞<j<∞∼,n≧1, be a sequence of stationary sequences on some probability space, with nonnegative random variables. Under appropriate mixing conditions, it is shown thatSn=$ X_{n,1} $+…+Xn,n has a limiting distribution of a general infinitely divisible form. The result is applied to sequences of functions {fn(x)∼ defined on a stationary sequence {Xj∼, whereXn.f=$ f_{n} $($ X_{j} $). The results are illustrated by applications to Gaussian processes, Markov processes and some autoregressive processes of a general type. Enthalten in Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers-Plenum Publishers, 1949 36(1984), 2 vom: 01. Dez., Seite 301-321 (DE-627)129934658 (DE-600)390313-8 (DE-576)015492907 0020-3157 nnns volume:36 year:1984 number:2 day:01 month:12 pages:301-321 https://doi.org/10.1007/BF02481972 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2012 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4316 GBV_ILN_4323 GBV_ILN_4324 AR 36 1984 2 01 12 301-321 |
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Summary Let {Xn,j,−∞<j<∞∼,n≧1, be a sequence of stationary sequences on some probability space, with nonnegative random variables. Under appropriate mixing conditions, it is shown thatSn=$ X_{n,1} $+…+Xn,n has a limiting distribution of a general infinitely divisible form. The result is applied to sequences of functions {fn(x)∼ defined on a stationary sequence {Xj∼, whereXn.f=$ f_{n} $($ X_{j} $). The results are illustrated by applications to Gaussian processes, Markov processes and some autoregressive processes of a general type. © The Institute of Statistical Mathematics, Tokyo 1984 |
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Summary Let {Xn,j,−∞<j<∞∼,n≧1, be a sequence of stationary sequences on some probability space, with nonnegative random variables. Under appropriate mixing conditions, it is shown thatSn=$ X_{n,1} $+…+Xn,n has a limiting distribution of a general infinitely divisible form. The result is applied to sequences of functions {fn(x)∼ defined on a stationary sequence {Xj∼, whereXn.f=$ f_{n} $($ X_{j} $). The results are illustrated by applications to Gaussian processes, Markov processes and some autoregressive processes of a general type. © The Institute of Statistical Mathematics, Tokyo 1984 |
| abstract_unstemmed |
Summary Let {Xn,j,−∞<j<∞∼,n≧1, be a sequence of stationary sequences on some probability space, with nonnegative random variables. Under appropriate mixing conditions, it is shown thatSn=$ X_{n,1} $+…+Xn,n has a limiting distribution of a general infinitely divisible form. The result is applied to sequences of functions {fn(x)∼ defined on a stationary sequence {Xj∼, whereXn.f=$ f_{n} $($ X_{j} $). The results are illustrated by applications to Gaussian processes, Markov processes and some autoregressive processes of a general type. © The Institute of Statistical Mathematics, Tokyo 1984 |
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Limiting distribution of sums of nonnegative stationary random variables |
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