### Skapa referens, olika format (klipp och klistra)

**Harvard**

Molchanov, I. och Zuyev, S. (2016) *Variational Analysis of Poisson Processes*.

** BibTeX **

@inbook{

Molchanov2016,

author={Molchanov, I. and Zuyev, Sergei},

title={Variational Analysis of Poisson Processes},

booktitle={Stochastic Analysis for Poisson Point Processes},

isbn={978-3-319-05232-8},

pages={81-101},

abstract={© 2016 Springer International Publishing Switzerland.The expected value of a functional F(η) of a Poisson process η can be considered as a function of its intensity measure μ. The paper surveys several results concerning differentiability properties of this functional on the space of signed measures with finite total variation. Then, necessary conditions for μ being a local minima of the considered functional are elaborated taking into account possible constraints on μ, most importantly the case of μ with given total mass a. These necessary conditions can be phrased by requiring that the gradient of the functional (being the expected first difference) is constant on the support of μ. In many important cases, the gradient depends only on the local structure of μ in a neighbourhood of x and so it is possible to work out the asymptotics of the minimising measure with the total mass a growing to infinity. Examples include the optimal approximation of convex functions, clustering problem and optimal search. In non-asymptotic cases, it is in general possible to find the optimal measure using steepest descent algorithms which are based on the obtained explicit form of the gradient.},

year={2016},

}

** RefWorks **

RT Book, Section

SR Electronic

ID 248973

A1 Molchanov, I.

A1 Zuyev, Sergei

T1 Variational Analysis of Poisson Processes

YR 2016

T2 Stochastic Analysis for Poisson Point Processes

SN 978-3-319-05232-8

SP 81

AB © 2016 Springer International Publishing Switzerland.The expected value of a functional F(η) of a Poisson process η can be considered as a function of its intensity measure μ. The paper surveys several results concerning differentiability properties of this functional on the space of signed measures with finite total variation. Then, necessary conditions for μ being a local minima of the considered functional are elaborated taking into account possible constraints on μ, most importantly the case of μ with given total mass a. These necessary conditions can be phrased by requiring that the gradient of the functional (being the expected first difference) is constant on the support of μ. In many important cases, the gradient depends only on the local structure of μ in a neighbourhood of x and so it is possible to work out the asymptotics of the minimising measure with the total mass a growing to infinity. Examples include the optimal approximation of convex functions, clustering problem and optimal search. In non-asymptotic cases, it is in general possible to find the optimal measure using steepest descent algorithms which are based on the obtained explicit form of the gradient.

LA eng

DO 10.1007/978-3-319-05233-5_3

LK http://dx.doi.org/10.1007/978-3-319-05233-5_3

OL 30