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Angaben zur Quelle [Bearbeiten]

Autor     D. Daley, D. Vere-Jones
Titel    An Introduction to the Theory of Point Processes. Volume I: Elementary Theory and Methods.
Ort    New York, Berlin, Heidelberg
Verlag    Springer
Jahr    2003
Anmerkung    Auszugsweise hier verfügbar: http://www.scribd.com/doc/47110225/An-Introduction-to-the-Theory-of-Point-Processes
ISBN    0-387-95541-0
URL    http://books.google.de/books/about/An_Introduction_to_the_Theory_of_Point_P.html?hl=de&id=Ev2iXQKItpUC

Literaturverz.   

ja
Fußnoten    ja
Fragmente    8


Fragmente der Quelle:
[1.] Rh/Fragment 090 38 - Diskussion
Zuletzt bearbeitet: 2012-08-07 17:23:22 Hindemith
Daley VereJones 2003, Fragment, Gesichtet, Rh, SMWFragment, Schutzlevel sysop, Verschleierung

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Untersuchte Arbeit:
Seite: 90, Zeilen: 38-40
Quelle: Daley VereJones 2003
Seite(n): 157, Zeilen: 20-25
These processes could be already covered formally by the general theory of point processes, as they can be represented as a special type of point process on a product space. However, marked [point processes are worth additional studying because of their wide range of applications and their conceptual importance.] Such processes are already covered formally by the general theory, as they can be represented as a special type of point process on a product space. However, marked point processes are deserving of study in their own right because of their wide range of applications, such as in queueing theory, and their conceptual importance [...]
Anmerkungen

Kein Quellenverweis vorhanden

Sichter
(Hindemith) Plagiatsfischer

[2.] Rh/Fragment 092 05 - Diskussion
Zuletzt bearbeitet: 2012-07-31 20:59:46 WiseWoman
Daley VereJones 2003, Fragment, Gesichtet, Rh, SMWFragment, Schutzlevel sysop, Verschleierung

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Seite: 92, Zeilen: 5-25
Quelle: Daley VereJones 2003
Seite(n): 195;202, Zeilen: 1-13,24-25,35-38;13-17
There exists a rich class of MPPs with a great variety of forms that can be taken by the marks and the variety of dependence relations among marks and locations. Two important classes are defined below

[...]

The next definition characterizes two important types of independence relating to the mark structure of MPPs.

[...]

Of course the most common case of an MPP with independent marks occurs when the marks are iid. Similarly, the most common case of a process with unpredictable marks occurs when the marks are conditionally iid given the past of the process. The most interesting extensions appear when we drop the assumption of completely independent marks and consider ways in which either the marks can influence the future development of the process or the current state of the process can influence the distribution of marks, or both.

The class of MPPs is a great deal richer than might at first appear. This is due to the great variety of forms that can be taken by the marks and the variety of

dependence relations that can exist between the marks themselves and their locations. [...] we define for MPPs the following two classes of point processes.

[...]

The next pair of definitions characterize two important types of independence relating to the mark structure of MPPs.

[...]

The most common case of an MPP with independent marks occurs when the kappa_i are in fact i.i.d. Similarly, the most common case of a process with unpredictable marks occurs when the marks are conditionally i.i.d. given the past of the process [...]

The most interesting extensions appear when we drop the assumption of completely independent marks and consider ways in which either the marks can influence the future development of the process or the current state of the process can influence the distribution of marks, or both.

Anmerkungen

Die beiden Auslassungen in der Arbeit sind mathematische Definitionen, die eo ipso als mögliches Plagiat ausscheiden.

Auf S. 91 findet sich folgender Hinweis auf die Quelle: "The results shown in the next section are based on first volume of Daley and Vere-Jones (2003)." Siehe Diskussion.

Sichter
KnallErbse

[3.] Rh/Fragment 092 34 - Diskussion
Zuletzt bearbeitet: 2012-08-07 23:18:50 Hindemith
Daley VereJones 2003, Fragment, KeineWertung, Rh, SMWFragment, Schutzlevel, ZuSichten

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Seite(n): 183, Zeilen: 17-20
One of the most important characteristics of these processes is that they combine in the model both a cluster process representation and a simple conditional intensity representation, which is moreover linear. One reason for its versatility and popularity is that it combines in the one model both a cluster process representation and a simple conditional intensity representation, which is moreover linear.
Anmerkungen

Auf Seite 91 steht: "The results shown in the next section are based on first volume of Daley and Vere-Jones (2003).". Wörtliche Zitate sind davon aber nicht abgedeckt. Da die Übernahme sehr kurz ist, vorerst: "keine Wertung"

Sichter
(Hindemith)

[4.] Rh/Fragment 093 07 - Diskussion
Zuletzt bearbeitet: 2012-08-07 17:23:31 Hindemith
Daley VereJones 2003, Fragment, Gesichtet, Rh, SMWFragment, Schutzlevel sysop, Verschleierung

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Untersuchte Arbeit:
Seite: 93, Zeilen: 7-12
Quelle: Daley VereJones 2003
Seite(n): 184, Zeilen: 4-7, 21-24
The events immigrants arrive according to a Poisson process at the constant rate μ, while the offspring arise as elements of a finite Poisson process that is associated with some point already constructed.

An important task is to find conditions that ensure the existence of stationary in this process, i.e., of realizations of point sets {ti} on the whole space T = IR having structure above and with distribution invariant under translation.

Immigrants {yj}, say, arrive according to a Poisson process at constant rate μc, while the offspring arise as elements of a finite Poisson process that is associated with some point already constructed. [...]

An important task is to find conditions that ensure the existence of a stationary Hawkes process (i.e. of realizations of point sets {xi} on the whole space X = IRd having the structure above and with distributions invariant under translation).

Anmerkungen

Auf S. 91 findet sich folgender Hinweis auf die Quelle: "The results shown in the next section are based on first volume of Daley and Vere-Jones (2003)." Wörtliche Zitate sind damit aber nicht abgedeckt.

Die folgende Proposition 4.3.7. findet sich dann auch sehr ähnlich in der Quelle (Seite 203)

Sichter
(Hindemith) Plagiatsfischer

[5.] Rh/Fragment 096 28 - Diskussion
Zuletzt bearbeitet: 2012-08-11 20:46:00 WiseWoman
Daley VereJones 2003, Fragment, Gesichtet, Rh, SMWFragment, Schutzlevel sysop, Verschleierung

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Untersuchte Arbeit:
Seite: 96, Zeilen: 11-32
Quelle: Daley VereJones 2003
Seite(n): 229, 247, 248, Zeilen: 229: 13-14, 25-29, 21; 247: 40-42; 248: 1, 4-11, 25-34
PROPOSITION 4.3.13 [siehe Link ]

The essence of the approach for the likelihood of a MPP is the use of a causal description of the process through successive conditioning. For ease of writing, we use jn(t1,..., tn ∣ w) for the local Janossy density on the interval (0,w) and J0(w) for J0((0,k)) [sic, recte: J0((0,w))]. Furthermore, we define the intervals τi = ti — ti-1 for i ≥ l and t0 = 0, and the conditional survivor functions Sk(w ∣ t1,..., tk−1) = P(τk ∣t1,..., tk−1) [sic, recte: P(τk > w ∣t1,..., tk−1)] and observe that these can be represented recursively in terms of the Janossy functions through the equations

[GLEICHUNGEN, identisch zur Quelle, siehe hier ]

where the pi (∙) are the densities, suitably conditioned, for the locations in the ground process, and the fi (∙) refer to the densities, again suitably conditioned, for the marks.

[Seite 247]

Proposition 7.3.I. [siehe Link ]

[Seite 229, 13-14]

The essence of this approach is the use of a causal description of the process through successive conditionings.[...]

[Seite 229, 25-26]

For ease of writing, we use jn(t1,..., tn ∣ u) for the local Janossy density on the interval (0,u), and J0(u) for J0((0,u)).

[Seite 229, 21]

[...] the intervals τi = ti — ti-1, i ≥ l, t0 = 0, are taken [...]

[Seite 229, 27-29] Now introduce the conditional survivor functions Sk(u ∣ t1,..., tk−1) = Pr{τk > u ∣t1,..., tk−1} and observe that these can be represented recursively in terms of the (local) Janossy functions through the equations

[Seite 248]

[GLEICHUNGEN, siehe link ]

where the pi (∙) refer to the densities, suitably conditioned, for the locations in the ground process, and the fi (∙) refer to the densities, again suitably conditioned, for the marks.

Anmerkungen

Die PROPOSITION 4.3.13 in der Dissertation ist identisch zur Proposition 7.3.I. in der Quelle (wobei in der Dissertation eine äquivalente Aussage weggelassen wurde).

Ein Quellenverweis fehlt und auch nach der Proposition wird weiter übernommen. Dabei wird die Notation geringfügig geändert (u aus der Quelle wird zu w), wobei sich Fehler einschleichen (k anstatt w; > w vergessen).

Sichter
(Hindemith), (Plagiatsfischer), WiseWoman

[6.] Rh/Fragment 097 10 - Diskussion
Zuletzt bearbeitet: 2012-08-11 20:58:18 WiseWoman
Daley VereJones 2003, Fragment, Gesichtet, Rh, SMWFragment, Schutzlevel sysop, Verschleierung

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Untersuchte Arbeit:
Seite: 97, Zeilen: 10-33
Quelle: Daley VereJones 2003
Seite(n): 231, 248, 249, Zeilen: 231: 12-17; 248: 38; 249: 1-3, 6-25
The main aim of the Proposition 4.3.14 was to make conditional the distribution of the current marks as time progresses, on marks and time points of all preceding events, i.e., the full set of the time points (0, T), irrespective of the marks and their relative positions in time.

Another view to look at is through the hazard functions. Instead of specifying the conditional densities pn(∙∣∙) as in (4.3.10) we express them in terms of their hazard functions

[GLEICHUNGEN, identisch zur Quelle, siehe link ]

Using the conditioning in the hazard functions may now include the values of the preceeding marks as well as the length of the current and preceeding intervals. Thus, all the information is summarized in the internal history H ≡ {Ht : t ≥ 0} of the process and of this form the amalgam of hazard function functions [sic] and mark densities can be represented as a single composite function for the MPP as follows

[GLEICHUNG, identisch zur Quelle, siehe link ]

where h1(t) is the hazard function for the location of the initial point, h2(t∣(t1, x1)) the hazard function for the location of the second point conditioned by the location of the first point and the value of the first mark, and so on, while f1(x∣t) is the density for the first mark given its location, and so on.

Hence a regular MPP N on R+ × X can be represented piecewise by the function λ*(t, x) named the conditional intensity function with respect to its internal history H.

Predictability, as it was defined in (4.3.5), is important in it that the hazard functions refer to the risk at the end of a time interval, not at the beginning of the next interval.

[Seite 248: 38]

In the equations above we condition the distribution of the current mark, as

[Seite 249: 1-3]

time progresses, on both marks and time points of all preceding events; in the proposition, we condition on the full set of time points in (0, T), irrespective of the marks and of their relative positions in time.

[Seite 231: 12-17]

We now make a seemingly innocuous but critical shift of view. Instead of specifying the conditional densities pn(∙∣∙) directly, we express them in terms of their hazard functions

[GLEICHUNGEN, siehe (7.2.2) ]

[Seite 249: 6-25]

The conditioning in the hazard functions may now include the values of the preceding marks as well as the length of the current and preceding intervals. All this information is collected into the internal history H ≡ {Ht : t ≥ 0} of the process so that the amalgam of hazard functions and mark densities can be represented as a single composite function for the MPP, namely

[GLEICHUNG, siehe (7.3.2) ]

where h1(t) is the hazard function for the location of the initial point, h2(t∣(t1, κ1)) the hazard function for the location of the second point conditioned by the location of the first point and the value of the first mark, and so on, while f1(κ∣t) is the density for the first mark given its location, and so on.

Definition 7.3.II. Let N be a regular MPP on R+ × K. The conditional intensity function for N, with respect to its internal history H, is the representative function λ*(t, κ) defined piecewise by (7.3.2).

Predictability is again important in that the hazard functions refer to the risk at the end of a time interval, not at the beginning of the next time interval, [...]

Anmerkungen

Ein Quellenverweis fehlt.

Sichter
(Hindemith), WiseWoman

[7.] Rh/Fragment 098 01 - Diskussion
Zuletzt bearbeitet: 2012-08-09 18:58:07 Hindemith
Daley VereJones 2003, Fragment, Gesichtet, Rh, SMWFragment, Schutzlevel sysop, Verschleierung

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Quelle: Daley VereJones 2003
Seite(n): 249, Zeilen: 25-27, 29-33, 38
[Similarly,] the conditional mark density refers to the distribution to be anticipated at the end of a time interval, not immediately after the next interval has begun.

Other form to write λ*(t,x) is through the H-intensity of the ground process and the conditional density of a mark at t given Ht−

Rh Page 098 diss.png

Similarly, the conditional mark density refers to the distribution to be anticipated at the end of a time interval, not immediately after the next interval has begun. [...]

It is often convenient to write

λ*(t,κ) = λ*g(t) f*(κ∣t) , (7.3.3)

where λ*g(t) is the H-intensity of the ground process [...], and f*(κ∣t) is the conditional density of a mark at t given Ht− [...]

Rh Page 098 Dale Vere-Jones 2003.png

Anmerkungen

Eine Quellenangabe fehlt. Die Übernahme beginnt auf der Vorseite: Rh/Fragment 097 10

Sichter
(Hindemith) Plagiatsfischer

[8.] Rh/Fragment 098 15 - Diskussion
Zuletzt bearbeitet: 2012-08-08 16:28:43 Hindemith
Daley VereJones 2003, Fragment, Gesichtet, Rh, SMWFragment, Schutzlevel sysop, Verschleierung

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Seite(n): 252, Zeilen: 10-14
Notice, that in a process with independent marks, the ground process and the marks are completely independent, whereas for a process with unpredictable marks, the marks can influence the subsequent evolution of the process, though the ground process does not influence the distribution of the marks. In a process with independent marks, the ground process and the marks are completely decoupled (i.e. they are independent processes), whereas for a process with unpredictable marks, the marks can influence the subsequent evolution of the process, though the ground process does not influence the distribution of the marks.
Anmerkungen

Es ist keine Quellenangabe vorhanden. Auch die Proposition 4.3.15, die der Fundstelle vorrausgeht, ist in der Quelle vor der hier dokumentierten Passage zu finden (Proposition 7.3.V).

Sichter
(Plagiatsfischer), Hindemith

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