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...ma</math>-[[sigma finite measure|finite measure]] <math>\mu</math>. The '''Poisson random measure''' with intensity [[Measure (mathematics)|measure]] <math>\m i) <math>\forall A\in\mathcal{A},\quad N_A</math> is a [[Poisson distribution|Poisson random variable]] with rate <math>\mu(A)</math>. ...

...e article lacks a definition, illustrative examples, but is of importance (Poisson process, Lévy process)|date=December 2013}} ...nd Poisson]] process.<ref>Tankov, P. (2003). Financial modelling with jump processes (Vol. 2). CRC press.</ref> ...

{{Short description|Poisson point process}} ...Poisson process''' is a [[point process]] which is a generalization of a [[Poisson process]] where the intensity that varies across the underlying mathematica ...

...ndom, with a specified probability distribution. To be precise, a compound Poisson process, parameterised by a rate <math>\lambda > 0</math> and jump size dis where, <math> \{\,N(t) : t \geq 0\,\}</math> is the counting variable of a [[Poisson process]] with rate <math>\lambda</math>, and <math> \{\,D_i : i \geq 1\,\} ...

==Stochastic processes topics== :''This list is currently incomplete.'' See also [[:Category:Stochastic processes]] ...

...additive process]]<ref>{{cite book |last1=Sato |first1=Ken-Ito |title=Lévy processes and infinitely divisible distributions |date=1999 |pages=31-68|publisher=Ca and the [[Poisson point process]]. ...

{{Short description|Generalization of Markov jump processes}} ...are special cases among the more general class of [[Renewal theory|renewal processes]]. ...

...ef>{{Cite book |last=Le Gall |first=Jean-François |title=Spatial branching processes, random snakes, and partial differential equations |publisher=Springer Scie ...g sub-trees generated by finitely many leaves, using a Brownian excursion, Poisson separating a straight line or as a limit of Galton-Watson trees. ...

...]] with independent, stationary increments: it represents the motion of a point whose successive displacements are [[random variable|random]], in which dis ...itive process]]es.<ref>{{cite book |last1=Sato |first1=Ken-Iti |title=Lévy processes and infinitely divisible distributions |date=1999 |pages=31-68|publisher=Ca ...

...3">D. J. Daley and D. Vere-Jones. ''An introduction to the theory of point processes. Vol. I''. Probability and its Applications (New York). Springer, New York, ===Poisson distribution=== ...

*[[Business process modeling]], activity of representing processes of an enterprise in order to deliver improvements ...uctural design of processes, applies to fields such as computers, business processes, logistics, project management ...

...Barndorff-Nielsen]], who studied it in the context of physics of [[Aeolian processes|wind-blown sand]].<ref>{{cite journal|doi=10.1098/rspa.1977.0041|last=Barnd ...ic at one point in time might fail to be generalized hyperbolic at another point in time. In fact, the generalized Laplace distributions and the normal inve ...

...a represents the <math>n</math>th [[moment (mathematics)|moment]] of the [[Poisson distribution]] with [[mean]] 1. Sometimes Dobiński's formula is stated as s ...near algebra, but it is enlightening to introduce a [[Poisson distribution|Poisson-distributed]] [[random variable]] <math>X</math> with [[mean]] 1. The equa ...

===Poisson=== ...binomial distribution]] can be proposed instead, in which the mean of the Poisson distribution can itself be thought of as a random variable drawn – in this ...

For a [[Poisson point process| Poisson counting process]], the variance in the count equals the mean count, so <ma === Example: Poisson Counting Process === ...

...aley, D.J, Vere-Jones, D. (1988). ''An Introduction to the Theory of Point Processes''. Springer, New York. {{isbn|0-387-96666-8}}, {{MR|950166}}.</ref> ...ribed completely by the (random) intervals between the points. These point processes are frequently used as models for random events in time, such as the arriva ...

...a particular plot of land. More complicated forms of data include marked point sets and spatial [[time series]]. The coordinate-wise mean of a point set is the [[centroid]], which solves the same [[central tendency#Solutions ...

...s, it is also used as a diagnostic in [[computer simulations]] of physical processes. The electric field created by a point charge ''q'' is ...

In [[statistics]], '''Poisson regression''' is a [[generalized linear model]] form of [[regression analys ...alue]] can be modeled by a linear combination of unknown [[parameter]]s. A Poisson regression model is sometimes known as a [[log-linear model]], especially w ...

...l theory''' is the branch of [[probability theory]] that generalizes the [[Poisson process]] for arbitrary holding times. Instead of [[exponential distributio .../math> with a suitable non-negative function. The superposition of renewal processes can be studied as a special case of [[Markov renewal process]]es. ...