Some Remarks on Definitions of Memory for Stationary Random Processes and Fields
Abstract In the paper, we discuss how to define long, short, and negative memories for stationary processes on ℤ and fields on $ ℤ^{d} $ with infinite variances. We propose to distinguish the properties of dependence and memory, and to attribute memory properties not only to a stationary random proc...
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Gespeichert in:
| Autor*in: |
Paulauskas, Vygantas [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media New York 2016 |
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| Übergeordnetes Werk: |
Enthalten in: Lithuanian mathematical journal - Springer US, 1975, 56(2016), 2 vom: Apr., Seite 229-250 |
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| Übergeordnetes Werk: |
volume:56 ; year:2016 ; number:2 ; month:04 ; pages:229-250 |
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| DOI / URN: |
10.1007/s10986-016-9316-1 |
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OLC2069939030 |
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| 520 | |a Abstract In the paper, we discuss how to define long, short, and negative memories for stationary processes on ℤ and fields on $ ℤ^{d} $ with infinite variances. We propose to distinguish the properties of dependence and memory, and to attribute memory properties not only to a stationary random process (or a field) but also to a process and the operation that we apply to this process. We deal exclusively with the summation operation, that is, we consider the limit behavior of partial sums of random processes or fields. In order to have a unified approach to processes and fields with finite and infinite variances, we propose to define memory properties via the growth of normalizing sequences in limit theorems for partial sums. Also, we propose to change a little bit the terminology: instead of terms “long and short memories,” to use positive and zero memories, respectively, leaving the term “negative memory” and introducing “strongly negative memory.” For random fields, we introduce the notions of isotropic and directional memories. | ||
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10.1007/s10986-016-9316-1 doi (DE-627)OLC2069939030 (DE-He213)s10986-016-9316-1-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Paulauskas, Vygantas verfasserin aut Some Remarks on Definitions of Memory for Stationary Random Processes and Fields 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2016 Abstract In the paper, we discuss how to define long, short, and negative memories for stationary processes on ℤ and fields on $ ℤ^{d} $ with infinite variances. We propose to distinguish the properties of dependence and memory, and to attribute memory properties not only to a stationary random process (or a field) but also to a process and the operation that we apply to this process. We deal exclusively with the summation operation, that is, we consider the limit behavior of partial sums of random processes or fields. In order to have a unified approach to processes and fields with finite and infinite variances, we propose to define memory properties via the growth of normalizing sequences in limit theorems for partial sums. Also, we propose to change a little bit the terminology: instead of terms “long and short memories,” to use positive and zero memories, respectively, leaving the term “negative memory” and introducing “strongly negative memory.” For random fields, we introduce the notions of isotropic and directional memories. stationary random processes stationary random fields memory Enthalten in Lithuanian mathematical journal Springer US, 1975 56(2016), 2 vom: Apr., Seite 229-250 (DE-627)130618624 (DE-600)795211-9 (DE-576)016125312 0363-1672 nnns volume:56 year:2016 number:2 month:04 pages:229-250 https://doi.org/10.1007/s10986-016-9316-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 56 2016 2 04 229-250 |
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10.1007/s10986-016-9316-1 doi (DE-627)OLC2069939030 (DE-He213)s10986-016-9316-1-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Paulauskas, Vygantas verfasserin aut Some Remarks on Definitions of Memory for Stationary Random Processes and Fields 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2016 Abstract In the paper, we discuss how to define long, short, and negative memories for stationary processes on ℤ and fields on $ ℤ^{d} $ with infinite variances. We propose to distinguish the properties of dependence and memory, and to attribute memory properties not only to a stationary random process (or a field) but also to a process and the operation that we apply to this process. We deal exclusively with the summation operation, that is, we consider the limit behavior of partial sums of random processes or fields. In order to have a unified approach to processes and fields with finite and infinite variances, we propose to define memory properties via the growth of normalizing sequences in limit theorems for partial sums. Also, we propose to change a little bit the terminology: instead of terms “long and short memories,” to use positive and zero memories, respectively, leaving the term “negative memory” and introducing “strongly negative memory.” For random fields, we introduce the notions of isotropic and directional memories. stationary random processes stationary random fields memory Enthalten in Lithuanian mathematical journal Springer US, 1975 56(2016), 2 vom: Apr., Seite 229-250 (DE-627)130618624 (DE-600)795211-9 (DE-576)016125312 0363-1672 nnns volume:56 year:2016 number:2 month:04 pages:229-250 https://doi.org/10.1007/s10986-016-9316-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 56 2016 2 04 229-250 |
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10.1007/s10986-016-9316-1 doi (DE-627)OLC2069939030 (DE-He213)s10986-016-9316-1-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Paulauskas, Vygantas verfasserin aut Some Remarks on Definitions of Memory for Stationary Random Processes and Fields 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2016 Abstract In the paper, we discuss how to define long, short, and negative memories for stationary processes on ℤ and fields on $ ℤ^{d} $ with infinite variances. We propose to distinguish the properties of dependence and memory, and to attribute memory properties not only to a stationary random process (or a field) but also to a process and the operation that we apply to this process. We deal exclusively with the summation operation, that is, we consider the limit behavior of partial sums of random processes or fields. In order to have a unified approach to processes and fields with finite and infinite variances, we propose to define memory properties via the growth of normalizing sequences in limit theorems for partial sums. Also, we propose to change a little bit the terminology: instead of terms “long and short memories,” to use positive and zero memories, respectively, leaving the term “negative memory” and introducing “strongly negative memory.” For random fields, we introduce the notions of isotropic and directional memories. stationary random processes stationary random fields memory Enthalten in Lithuanian mathematical journal Springer US, 1975 56(2016), 2 vom: Apr., Seite 229-250 (DE-627)130618624 (DE-600)795211-9 (DE-576)016125312 0363-1672 nnns volume:56 year:2016 number:2 month:04 pages:229-250 https://doi.org/10.1007/s10986-016-9316-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 56 2016 2 04 229-250 |
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Abstract In the paper, we discuss how to define long, short, and negative memories for stationary processes on ℤ and fields on $ ℤ^{d} $ with infinite variances. We propose to distinguish the properties of dependence and memory, and to attribute memory properties not only to a stationary random process (or a field) but also to a process and the operation that we apply to this process. We deal exclusively with the summation operation, that is, we consider the limit behavior of partial sums of random processes or fields. In order to have a unified approach to processes and fields with finite and infinite variances, we propose to define memory properties via the growth of normalizing sequences in limit theorems for partial sums. Also, we propose to change a little bit the terminology: instead of terms “long and short memories,” to use positive and zero memories, respectively, leaving the term “negative memory” and introducing “strongly negative memory.” For random fields, we introduce the notions of isotropic and directional memories. © Springer Science+Business Media New York 2016 |
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Abstract In the paper, we discuss how to define long, short, and negative memories for stationary processes on ℤ and fields on $ ℤ^{d} $ with infinite variances. We propose to distinguish the properties of dependence and memory, and to attribute memory properties not only to a stationary random process (or a field) but also to a process and the operation that we apply to this process. We deal exclusively with the summation operation, that is, we consider the limit behavior of partial sums of random processes or fields. In order to have a unified approach to processes and fields with finite and infinite variances, we propose to define memory properties via the growth of normalizing sequences in limit theorems for partial sums. Also, we propose to change a little bit the terminology: instead of terms “long and short memories,” to use positive and zero memories, respectively, leaving the term “negative memory” and introducing “strongly negative memory.” For random fields, we introduce the notions of isotropic and directional memories. © Springer Science+Business Media New York 2016 |
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Abstract In the paper, we discuss how to define long, short, and negative memories for stationary processes on ℤ and fields on $ ℤ^{d} $ with infinite variances. We propose to distinguish the properties of dependence and memory, and to attribute memory properties not only to a stationary random process (or a field) but also to a process and the operation that we apply to this process. We deal exclusively with the summation operation, that is, we consider the limit behavior of partial sums of random processes or fields. In order to have a unified approach to processes and fields with finite and infinite variances, we propose to define memory properties via the growth of normalizing sequences in limit theorems for partial sums. Also, we propose to change a little bit the terminology: instead of terms “long and short memories,” to use positive and zero memories, respectively, leaving the term “negative memory” and introducing “strongly negative memory.” For random fields, we introduce the notions of isotropic and directional memories. © Springer Science+Business Media New York 2016 |
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