P. BREMAUD, CEREMADE, Universite de Paris IX (Dauphine). Abstract Optimal stochastic control of point processes (and more generally of marked. Increas- ingly, spatial-temporal point processes are used to describe environmental process. This sort of definition is used by Jacod (), Brémaud (). Authors; Authors and affiliations. P. Bremaud Point Process Counting Process Jump Process Stochastic Integration Local Martingale. These keywords were.

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Probability and random processes. Prrocesses random sums over point processes have applications in many areas where they are used as mathematical models. This article is also available for rental through DeepDyve. From inside the book. Probability and its Applications.

Article PDF first page preview. Email alerts New issue alert. Likelihood Ratios and Martingale. From this theorem some expectation results for the Poisson point process follow, including its Laplace functional. A multiplicative analogue of Schnirelmann’s theorem. Stochastic pount and its applicationsvolume 2. You do not currently have access to this article. Palm Martingale calculus and stochastic recurrences.

Sign In Forgot password? Consequently, the study of random sums of functions over point processes is known as shot noise in probability and, particularly, point process theory. If the function is a function of more than one point of the point process, the moment measures or factorial moment measures of the point process are needed, which can processez compared to moments and factorial of random variables.

Point processes and queues, martingale dynamics in SearchWorks catalog

Lecture Notes in Mathematics. Fourier Analysis of Stochastic Processes. My library Help Advanced Book Search.


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Campbell’s theorem (probability)

Don’t have an account? University of California, Berkeley- Martingales Mathematics – pages. Another result by the name of Campbell’s theorem [7] is specifically for the Poisson point process and gives a method for calculating moments as well as the Laplace functional of a Poisson point process.

In wireless network communication, when a transmitter is trying to send a signal to a receiver, all the other transmitters in the network can be considered as interference, which poses a similar problem as noise does in traditional wired telecommunication networks in terms of the ability to send data based on information theory. For general point processes, other more general versions of Campbell’s theorem exist depending on the nature of the random sum and in particular the function being summed over the point process.

For general point processes, Campbell’s theorem is only for sums of functions of a single point of the point process. If you originally registered with a username please use that to sign in.

This equation naturally holds for the homogeneous Poisson point processes, which is an example of a stationary stochastic process. Lower bounds for the height in Galois extensions: From Wikipedia, the free encyclopedia. Sign in via your Institution Sign in. Sign In or Create an Account. Factorial moment measures are used when points are not allowed to repeat, hence points are distinct. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide.

Point Processes and Queues: Martingale Dynamics (Springer Series in Statistics) – Bremaud, P.

In probability theory and statisticsPoimt theorem or the Campbell—Hardy theorem is either a particular equation or set of results relating to the expectation of a function summed over a point process to an integral involving the mean measure of the point process, which allows for the calculation of expected value and variance of the random sum.


Continuum percolation, volume of Cambridge tracts in mathematics, By using this pont, you agree to the Terms of Use and Privacy Policy. Hardywhich has inspired the result to be sometimes called the Campbell—Hardy theorem. A Martingale Approach to Point Processes. Account Options Sign in. Application to Communication Theory. Foundations and Trends in Networking.

You could not be signed in. Common terms and phrases absolutely continuous adapted to Fe,t basic measurable space bounded bounded variation Brownian motion continuous with respect corrupted by white Definition ii dispatching equation exp iu F,Fe family Fe filtering function Girsanov theorem innovation theorem jumps Kunita and Watanabe L2 martingale left continuous Lemma Let Q Markov chain Markov process martingale characterization martingale theory measurable process adapted Meyer Meyer’s decomposition modulating mutual information natural increasing process p,Fe paragraph probability measure probability space problem process with rate proof random rate random variable right continuous paths right continuous step self-exciting point process Snyder space of point space Q square integrable martingale standard Poisson process step process Stieltjes integral stochastic differential equations stochastic integral Stochastic Processes Theorem B.

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Retrieved from ” https: The name of both theorems stems from the work [8] [9] by Norman R.