Zur Überlagerung von Erneuerungsprozessen
Summary If a finite sequence of independent (not necessarily stationary) renewal processes is given, a superposition process can easily be defined as the union of all point sequences represented by the given processes. The properties of such superposition processes are investigated. First, a necessa...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
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| Format: |
E-Artikel |
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| Sprache: |
Deutsch |
| Erschienen: |
1969 |
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| Umfang: |
16 |
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| Reproduktion: |
Springer Online Journal Archives 1860-2002 |
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| Übergeordnetes Werk: |
in: Probability theory and related fields - 1992, 13(1969) vom: Jan., Seite 9-24 |
| Übergeordnetes Werk: |
volume:13 ; year:1969 ; month:01 ; pages:9-24 ; extent:16 |
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NLEJ205658253 |
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| 520 | |a Summary If a finite sequence of independent (not necessarily stationary) renewal processes is given, a superposition process can easily be defined as the union of all point sequences represented by the given processes. The properties of such superposition processes are investigated. First, a necessary and sufficient condition for a superposition process to be a renewal process is given. Essentially, this condition reads thus: the given processes must be Poisson processes. The main result given in this paper is a limit theorem for superposition processes which shows that, even with largely arbitrary renewal processes superimposed, the superposition process has local properties which approach the properties of the Poisson process as the number of given processes increases. The theorem contains some well-known special theorems of this type [e.g. Khintchine, 1960; Franken, 1963]. | ||
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(DE-627)NLEJ205658253 DE-627 ger DE-627 rakwb ger Zur Überlagerung von Erneuerungsprozessen 1969 16 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Summary If a finite sequence of independent (not necessarily stationary) renewal processes is given, a superposition process can easily be defined as the union of all point sequences represented by the given processes. The properties of such superposition processes are investigated. First, a necessary and sufficient condition for a superposition process to be a renewal process is given. Essentially, this condition reads thus: the given processes must be Poisson processes. The main result given in this paper is a limit theorem for superposition processes which shows that, even with largely arbitrary renewal processes superimposed, the superposition process has local properties which approach the properties of the Poisson process as the number of given processes increases. The theorem contains some well-known special theorems of this type [e.g. Khintchine, 1960; Franken, 1963]. Springer Online Journal Archives 1860-2002 Störmer, Horand oth in Probability theory and related fields 1992 13(1969) vom: Jan., Seite 9-24 (DE-627)NLEJ188987940 (DE-600)1462994-x 1432-2064 nnns volume:13 year:1969 month:01 pages:9-24 extent:16 http://dx.doi.org/10.1007/BF00535794 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 13 1969 1 9-24 16 |
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(DE-627)NLEJ205658253 DE-627 ger DE-627 rakwb ger Zur Überlagerung von Erneuerungsprozessen 1969 16 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Summary If a finite sequence of independent (not necessarily stationary) renewal processes is given, a superposition process can easily be defined as the union of all point sequences represented by the given processes. The properties of such superposition processes are investigated. First, a necessary and sufficient condition for a superposition process to be a renewal process is given. Essentially, this condition reads thus: the given processes must be Poisson processes. The main result given in this paper is a limit theorem for superposition processes which shows that, even with largely arbitrary renewal processes superimposed, the superposition process has local properties which approach the properties of the Poisson process as the number of given processes increases. The theorem contains some well-known special theorems of this type [e.g. Khintchine, 1960; Franken, 1963]. Springer Online Journal Archives 1860-2002 Störmer, Horand oth in Probability theory and related fields 1992 13(1969) vom: Jan., Seite 9-24 (DE-627)NLEJ188987940 (DE-600)1462994-x 1432-2064 nnns volume:13 year:1969 month:01 pages:9-24 extent:16 http://dx.doi.org/10.1007/BF00535794 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 13 1969 1 9-24 16 |
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(DE-627)NLEJ205658253 DE-627 ger DE-627 rakwb ger Zur Überlagerung von Erneuerungsprozessen 1969 16 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Summary If a finite sequence of independent (not necessarily stationary) renewal processes is given, a superposition process can easily be defined as the union of all point sequences represented by the given processes. The properties of such superposition processes are investigated. First, a necessary and sufficient condition for a superposition process to be a renewal process is given. Essentially, this condition reads thus: the given processes must be Poisson processes. The main result given in this paper is a limit theorem for superposition processes which shows that, even with largely arbitrary renewal processes superimposed, the superposition process has local properties which approach the properties of the Poisson process as the number of given processes increases. The theorem contains some well-known special theorems of this type [e.g. Khintchine, 1960; Franken, 1963]. Springer Online Journal Archives 1860-2002 Störmer, Horand oth in Probability theory and related fields 1992 13(1969) vom: Jan., Seite 9-24 (DE-627)NLEJ188987940 (DE-600)1462994-x 1432-2064 nnns volume:13 year:1969 month:01 pages:9-24 extent:16 http://dx.doi.org/10.1007/BF00535794 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 13 1969 1 9-24 16 |
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(DE-627)NLEJ205658253 DE-627 ger DE-627 rakwb ger Zur Überlagerung von Erneuerungsprozessen 1969 16 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Summary If a finite sequence of independent (not necessarily stationary) renewal processes is given, a superposition process can easily be defined as the union of all point sequences represented by the given processes. The properties of such superposition processes are investigated. First, a necessary and sufficient condition for a superposition process to be a renewal process is given. Essentially, this condition reads thus: the given processes must be Poisson processes. The main result given in this paper is a limit theorem for superposition processes which shows that, even with largely arbitrary renewal processes superimposed, the superposition process has local properties which approach the properties of the Poisson process as the number of given processes increases. The theorem contains some well-known special theorems of this type [e.g. Khintchine, 1960; Franken, 1963]. Springer Online Journal Archives 1860-2002 Störmer, Horand oth in Probability theory and related fields 1992 13(1969) vom: Jan., Seite 9-24 (DE-627)NLEJ188987940 (DE-600)1462994-x 1432-2064 nnns volume:13 year:1969 month:01 pages:9-24 extent:16 http://dx.doi.org/10.1007/BF00535794 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 13 1969 1 9-24 16 |
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(DE-627)NLEJ205658253 DE-627 ger DE-627 rakwb ger Zur Überlagerung von Erneuerungsprozessen 1969 16 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Summary If a finite sequence of independent (not necessarily stationary) renewal processes is given, a superposition process can easily be defined as the union of all point sequences represented by the given processes. The properties of such superposition processes are investigated. First, a necessary and sufficient condition for a superposition process to be a renewal process is given. Essentially, this condition reads thus: the given processes must be Poisson processes. The main result given in this paper is a limit theorem for superposition processes which shows that, even with largely arbitrary renewal processes superimposed, the superposition process has local properties which approach the properties of the Poisson process as the number of given processes increases. The theorem contains some well-known special theorems of this type [e.g. Khintchine, 1960; Franken, 1963]. Springer Online Journal Archives 1860-2002 Störmer, Horand oth in Probability theory and related fields 1992 13(1969) vom: Jan., Seite 9-24 (DE-627)NLEJ188987940 (DE-600)1462994-x 1432-2064 nnns volume:13 year:1969 month:01 pages:9-24 extent:16 http://dx.doi.org/10.1007/BF00535794 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 13 1969 1 9-24 16 |
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Summary If a finite sequence of independent (not necessarily stationary) renewal processes is given, a superposition process can easily be defined as the union of all point sequences represented by the given processes. The properties of such superposition processes are investigated. First, a necessary and sufficient condition for a superposition process to be a renewal process is given. Essentially, this condition reads thus: the given processes must be Poisson processes. The main result given in this paper is a limit theorem for superposition processes which shows that, even with largely arbitrary renewal processes superimposed, the superposition process has local properties which approach the properties of the Poisson process as the number of given processes increases. The theorem contains some well-known special theorems of this type [e.g. Khintchine, 1960; Franken, 1963]. |
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Summary If a finite sequence of independent (not necessarily stationary) renewal processes is given, a superposition process can easily be defined as the union of all point sequences represented by the given processes. The properties of such superposition processes are investigated. First, a necessary and sufficient condition for a superposition process to be a renewal process is given. Essentially, this condition reads thus: the given processes must be Poisson processes. The main result given in this paper is a limit theorem for superposition processes which shows that, even with largely arbitrary renewal processes superimposed, the superposition process has local properties which approach the properties of the Poisson process as the number of given processes increases. The theorem contains some well-known special theorems of this type [e.g. Khintchine, 1960; Franken, 1963]. |
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Summary If a finite sequence of independent (not necessarily stationary) renewal processes is given, a superposition process can easily be defined as the union of all point sequences represented by the given processes. The properties of such superposition processes are investigated. First, a necessary and sufficient condition for a superposition process to be a renewal process is given. Essentially, this condition reads thus: the given processes must be Poisson processes. The main result given in this paper is a limit theorem for superposition processes which shows that, even with largely arbitrary renewal processes superimposed, the superposition process has local properties which approach the properties of the Poisson process as the number of given processes increases. The theorem contains some well-known special theorems of this type [e.g. Khintchine, 1960; Franken, 1963]. |
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