Talk:Point process

message: Can any experts provide more constructions for point processes, 
especially stationary ones on the entire line or plane ?
A construction for the real half-line is already given.
Is there any way to take 2 half-lines, with a Poisson process on each,
and somehow 'glue' them together to get one process on the whole line ?
The tricky part is the interval between the first points in each half-line.
If there's a way to do this gluing, I'd like to see it.
And what about the entire plane ?
Can you take the product of 2 independent Poisson processes on the entire line ?
--Kanyonman (talk) 13:10, 21 October 2008 (UTC)
thread_title:  constructions 

message: A point process is a stochastic process indexed by a sigma algebra of sets instead of a subset of the real line (time). But it is still a stochastic process in the general sense of the word. See, e.g., "Diffusions, Markov Processes and Martingales, Vol. 1" by Rogers and Williams, section II.33-37. There they treat Poisson point processes analogously to Brownian motion with a different indexing set. The Daniel-Kolmogorov theorem is applied to show existence of pre-Poisson set functions. Just as Brownian motion has extra properties that need to be satisfied (being a continuous function instead of just a function), the Poisson measure must also satisfy extra properties (being a measure instead of just a set function).  — Preceding unsigned comment added by Vinzklorthos (talk • contribs) 15:34, 15 November 2011 (UTC)
thread_title:  Point process as a stochastic process 

message: I'm sure this page is very nice and technically accurate and all, but it's couched in such abstract language as to be almost totally impenetrable by anyone who just wants a simple introduction to the concept as it might be used in an ordinary engineering or science context.  As such a user, I'm not qualified to actually fix this page myself, but to whomever is qualified to edit this page, please have some consideration for those of us who are not professional mathematicians!  69.205.70.143 (talk) 21:21, 29 July 2012 (UTC)
thread_title:  Usability issues with this page 

message: My reading of this is that a point process is defined over continuous time. Is that right? Mrdthree (talk) 03:27, 9 August 2013 (UTC)
thread_title: Discrete Time vs. Continuous Time Point Processes

message: Please can an expert edit the definition, in particular the notation and background around "that renders all the point counts"
This is opaque
Mlnsmonster (talk) 11:33, 1 July 2014 (UTC)
thread_title: opaque

message: It is written:
"Every point process ξ can be represented as
: \xi=\sum_{i=1}^N \delta_{X_i}, "
From the definition I don't see why it should be a finite sum.
Bongilles (talk) 14:16, 15 October 2013 (UTC)
thread_title:  Is the sum necesarily finite in the representation? 

message: Article makes no mention of invariant measure which is what point processes settle down into. No mention of chaos, many important processes are chaotic. No mention of shift spaces, which is the space in which point processes act. No mention of either transfer operators or Koopman operators, which describe the time evolution of point processes, when these are viewed as probability distributions. No examples of basic processes, e.g. the Bernoulli process. This is all standard introductory-textbook material for this topic. 67.198.37.16 (talk) 23:22, 11 May 2018 (UTC)
thread_title:  missing coverage of basic introductory topics 

message: In the section "General point process theory", the words "counting measure" link to Counting_measure which seems be accurate at first glance but I think the article Counting_measure describes a different concept (namely the measure that maps a set to its cardinality). Counting_measure defines *the* counting measure which is a specific measure. While on the present page, we talk about "the set of locally finite counting measures" which does not make sense if there is only one. I guess on the present page, *a* counting measure is any integer-valued measure (possibly subject to some restrictions). So the link to Counting_measure should be removed and a definition of "counting measure" added in the text (or the link could lead to a page describing counting measures in the sense of the present page). (I am not sufficiently familiar with point processes to do so myself.) Dominique Unruh (talk) 13:17, 28 September 2019 (UTC)
thread_title:  Wrong link for "counting measure"