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	Poisson process - Wikipedia, the free encyclopedia
		The Poisson process is a continuous-time process: its discrete-time counterpart is the Bernoulli process.
		A Poisson process is a pure-birth process, the simplest example of a birth-death process.
		Just as a Poisson random variable is characterized by its scalar parameter λ, a homogeneous Poisson process is characterized by its rate parameter λ, which is the expected number of "events" or "arrivals" that occur per unit time.
	en.wikipedia.org /wiki/Poisson_process (978 words)

	MUG: compound Poisson process (21.1.03) (Site not responding. Last check: 2007-10-10)
		OK, a compound Poisson process is defined by X(t) = sum_{i=1}^N(t) Y_i for t >= 0, where N(t) is a Poisson process and {Y_i} a family of iid random variables independent of N(t).
		By "generating" the process, I suppose what you want is to generate a sample from this process, i.e.
		Suppose the Poisson process N(t) has rate r, so for s < t, N(t) - N(s) is Poisson with parameter r*(t-s), and X(t) - X(s) is the sum of that many independent r.v.'s with the distribution for Y_i.
	www.math.rwth-aachen.de /mapleAnswers/html/1672.html (231 words)

	Syllabus query -- 2006/2007
		The students should identify the random walk, the homogeneous Poisson process, the non-homogeneous Poisson process, the compound Poisson process, the conditional Poisson process, renewal processes, regenerative processes, counting processes, discrete and continuous time Markov chains, Markov processes, Gaussian processes, the Brownian motion, processes with stationary increments, processes with independent increments, and queueing systems.
		Examples of stochastic processes: random walk; renewal and counting processes; Markov processes; stationary processes; processes with stationary and independent increments, and Gaussian processes.
		Poisson process: definitions.Instants of occurrence of events in Poisson processes.
	www.math.ist.utl.pt /prog.phtml?curso=09&disc=PrEs&sem=1&ano=4 (350 words)

	Learn Counting Process in 15 minutes!
		Constant intensity is a defining charactistic of a Poisson process.
		This is similar to nonhomogeneous Poisson process except we let you change g'(t) as you go, not neccessary according to a pre-determined pattern.
		In a compound Poisson process, the jump sizes are determined by Y_i, a sequence of independent random variables.
	www.ms.uky.edu /~mai/learn15.html (1072 words)

	Math 413
		A counting process is said to possess stationary increments if the distribution of number of events that occur in any time interval depends ONLY on the LENGTH of the time interval.
		Suppose we are told that exactly one event of a Poisson process has taken place by time t, and we want to determine the distribution of the time at which the event occurred.
		Now since a Poisson process possesses stationary and independent increments if seems reasonable that each interval in [0,t] of equal length should have the same probability of containing the event.
	www.cwu.edu /~chueh/math413_6.htm (700 words)

	Math 573 Actuarial Models I
		Calculate probabilities associated with a compound distribution when the compounding distribution is a member of the families in #3, and the compounded distribution is discrete or a discretization of a continuous distribution.
		Characterize the value of the process at a given time as a compound Poisson random variable.
		Define a Brownian motion process with drift and a geometric Brownian motion process.
	www.math.louisville.edu /actuarial/HTMLMath674.html (807 words)

	A Compound Poisson Process for Relaxing the Molecular Clock -- Huelsenbeck et al. 154 (4): 1879 -- Genetics
		The compound Poisson process discussed in this article places events of substitution-rate change on the tree according to a Poisson process.
		In this example, which illustrates the process for the tree from Fig 1, three events of substitution-rate change occur.
		process with exponential priors of means 1 and 10 (Fig 11).
	www.genetics.org /cgi/content/full/154/4/1879 (5895 words)

	Operational Risk - Models
		The event process for transaction handling errors is best approximated as a poisson process, in which the frequency of error events per unit of time is distributed as a poisson variable (although in theory, the exponential distribution could also be used to model the distribution of the time between errors).
		The mixture distribution is formulated as a compound poisson process.
		But the process is sure to develop, and the trend is likely to be towards bottom-up or hybrid models that, wherever possible, model the real workflows — despite the fact that it is harder to arrive at a full and consistent operational value-at-risk and capital allocation methodology by this means.
	www.financewise.com /public/edit/riskm/oprisk/opr-models.htm (1965 words)

	Poisson Processes
		X is a random process, such as those we have already met, but it has a continuous time parameter (t > 0), instead of a discrete one (n=0,1,...).
		The Poisson process is important because it forms a basis for extensions in a number of directions:
		The compound Poisson process is very important in insurance, as a model for the arrival of claims at an insurance office.
	www.staff.city.ac.uk /r.j.gerrard/courses/2dsm/dsm03_6.htm (370 words)

	Actuarial Modelling
		Handout on a compound Poisson process and ruin probability WITH ANSWERS.
		For a particular group of clients, a flow of claims arriving at an insurance company may be represented as a compound Poisson process, that is, we deal with the classical scheme.
		Let the amount of a particular claim be equal to either 2 or 3 or 4 with probabilities 1/4, 1/2, and 1/4, respectively.
	math.ucsd.edu /~vrotar/193a-h-ruin-a.html (287 words)

	BioMed Central \| Full text \| Gene capture prediction and overlap estimation in EST sequencing from one or multiple ...
		In this paper we propose a compound Poisson process approach for accurate prediction of gene capture in EST sequencing.
		The entries in the row of CPP or SR are the Mean and root of Mean Squared Error(rMSE) (in parentheses) based on 200 Monte Carlo samples.
		From this perspective, the compound Poisson process model can be regarded as a generalization or extension of the mixture model in [30].
	www.biomedcentral.com /1471-2105/6/300 (5804 words)

	Stochastic Processes: Appendix A (Site not responding. Last check: 2007-10-10)
		The Poisson process is a counting process in which interarrival times of successive jumps are independently and identically distributed (i.i.d.) exponential random variables.
		Karlin and Taylor ("A Second Course in Stochastic Processes", Academic Press, 1981), p.432, states "The general Lévy process can be represented as a sum of a Brownian motion, a uniform translation, and a limit (actually, an integral) of a one-parameter family of compound Poisson processes, where all the contributing basic processes are mutually independent".
		The connection with the Poisson process is the object of this section.
	www.puc-rio.br /marco.ind/stoch-a.html (4265 words)

	Inaugural Article: Distributional regimes for the number of k-word matches between two random sequences -- Lippert et ...
		Chen extended the concepts to Poisson approximation (17).
		The number of the islands is approximately Poisson.
		For the compound Poisson approximations in the nonuniform case,
	www.pnas.org /cgi/content/full/99/22/13980 (2468 words)

	The compound Poisson immigration process subject to binomial catastrophes, Antonis Economou
		However, under mild disastrous conditions, the appropriate model is a stochastic process subject to binomial catastrophes.
		In the present paper we consider a special such model in which a population evolves according to a compound Poisson process and catastrophes occur according to a renewal process.
		We study the equilibrium distribution of this process and we derive an algorithmic procedure for its approximate computation.
	projecteuclid.org /getRecord?id=euclid.jap/1082999082 (542 words)

	EconPapers: Statistical Models for High Frequency Security Prices
		This model can be viewed as a mixture of the compound Poisson process model by Press and the bid/ask bounce model by Roll.
		The second model generalizes the compound Poisson process to allow for an arbitrary dependence structure in its innovations so as to account for more complicated types of market microstructure.
		Comparison with actual high frequency data suggests that the proposed models are sufficiently flexible to capture a number of salient features of financial return data including a skewed and fat tailed marginal distribution, serial correlation at high frequency, time variation in market activity both at high and low frequency.
	econpapers.repec.org /paper/ecmnawm04/77.htm (367 words)

	Compound Poisson process approximation for locally dependent real-valued random variables via a new coupling ...
		Compound Poisson process approximation for locally dependent real-valued random variables via a new coupling inequality, Michael V. Boutsikas
		Compound Poisson process approximation for locally dependent real-valued random variables via a new coupling inequality
		[21] Wang, Y.H. (1989) From Poisson to compound Poisson approximations.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.bj/1151525133 (496 words)

	SEMINAR SERIES of ORCIBS / OPIS
		In the compound Poisson disorder problem, arrival rate and/or jump distribution of some compound Poisson process change suddenly at some unknown and unobservable time.
		We start observing the process, and the problem is to decide on the correct hypothesis as soon as possible and with the smallest probability of wrong decision.
		The customers arrive following a Poisson Process and each customer makes a purchasing decision based on her reservation prices of individual products: she either buys one of the individual products, buys the bundle or leaves without a purchase.
	home.ku.edu.tr /~opis/2005.html (4081 words)

	Compound Poisson process approximation (ResearchIndex)
		Abstract: Compound Poisson processes are often useful as approximate models, when describing the occurrence of rare events.
		Our approach is to use Stein's method directly, rather than by way of declumping and a marked Poisson process; this has conceptual advantages, but entails technical difficulties.
		1 Compound Poisson approximation for Markov chains using Stein..
	citeseer.ist.psu.edu /372590.html (359 words)

	Compound Poisson process - Wikipedia, the free encyclopedia
		A compound Poisson process with rate λ > 0 and jump size distribution G is a continuous-time stochastic process
		is a Poisson process with rate λ, and
		Using conditional expectation, the expected value of a compound Poisson process can be calculated as:
	en.wikipedia.org /wiki/Compound_Poisson_process (214 words)

	Derivation of the negative binomial distribution from the compound Poisson process (aka ``apparent contagion'') (via ... (Site not responding. Last check: 2007-10-10)
		Derivation of the negative binomial distribution from the compound Poisson process (aka ``apparent contagion'')
		In [2] Cliff and Ord explain the basic Poisson process, and then go on to describe the classical contagions, true (generalising) and apparent (compound), which are departures from the simple Poisson process (which produces Complete Spatial Randomness, or CSR).
		In this case, the clusters are distributed as Poisson, with the number of individuals in a cluster determined by the logarithmic distribution.
	zappa.nku.edu.cob-web.org:8888 /~longa/geomed/modules/ss1/lec/details/details.html (274 words)

	TxSpace at Texas A&M University Libraries: Item 1969.1/1499
		Three models were considered: a simple CPP using constant LET, a CPP using a chord length distribution, and a CPP using specific energy distribution.
		The dose rate sparing curve, representing surviving fraction at a dose of 10Gy vs. dose rate shows that deterministic survival results are consistent with stochastic survival results, using CPP, or CPP with chord length distribution, for low and high dose rate values.
		Compared to deterministic aspects of DNA damage formation we concluded that stochastic aspects of DNA damage formation and repair using CPP or CPP with chord length distribution are not as prominent as reported in the earlier studies.
	txspace.tamu.edu /handle/1969.1/1499 (406 words)

	Abstract (Site not responding. Last check: 2007-10-10)
		Optimality of an (s,S) Policy with Compound Poisson and Diffusion Demands: A Quasi-variational Inequalities Approach
		We prove that an (s, S) policy is optimal in a continuous-review stochastic inventory model with a fixed ordering cost when the demand is a mixture of (i) a diffusion process and a compound Poisson process with exponentially distributed jump sizes, and (ii) a constant demand and a compound Poisson process.
		Finally, the combination of a diffusion and a general compound Poisson demands is not completely solved.
	www.utdallas.edu /~sethi/Abstracts/abstract-QVI.htm (151 words)

	Compound Poisson process approximation, A. D. Barbour, Marianne Månsson
		Compound Poisson processes are often useful as approximate models, when describing the occurrence of rare events.
		BARBOUR, A. and LOH, W.-L. Compound Poisson approximation for non-negative random variables via Stein's method.
		ERHARDSSON, T. Compound Poisson approximation for Markov chains using Stein's method.
	projecteuclid.org /Dienst/UI/1.0/Display/euclid.aop/1029867135 (224 words)

	UM Department of Mathematics: Graduate Courses
		Geometric Brownian motion and the compound Poisson process.
		Special efforts will be made to attract and interest students in the rich diversity of applications of stochastic processes and to make them aware of the relevance and importance of the mathematical subtleties underlying stochastic processes.
		In both, a general theory is developed and detailed study is made of some special classes of processes and their applications.
	www.math.lsa.umich.edu /courses/grad.shtml (7354 words)

	Wick Calculus On Spaces Of Generalized Functions Of Compound Poisson White Noise - Lytvynov, Rebenko, Shchepan'uk ... (Site not responding. Last check: 2007-10-10)
		We derive white noise calculus for a compound Poisson process.
		6 the Poisson integral representation in the classical statist..
		2 Quantum compound Poisson processes and white noise calculus (context) - Lytvynov, Rebenko et al.
	citeseer.ist.psu.edu /191639.html (590 words)

	Toward a Neutral Evolutionary Model of Gene Expression -- Khaitovich et al. 170 (2): 929 -- Genetics
		describes mutations on the DNA level as a Poisson process and
		of gene expression is a compound Poisson process with independent
		processes with an asymmetric distribution of mutational effects.
	www.genetics.org /cgi/content/full/170/2/929 (4427 words)

	Stony Brook AMS - Downloadable Preprints, 2000 (Site not responding. Last check: 2007-10-10)
		In a typical model of this sort, in the absence of control, the reserve (surplus) process, which represents the liquid assets of the company, is governed by a Brownian motion with constant drift and diffusion coefficient.
		This is a limiting case of the classical Cramer-Lundberg model in which the reserve is a compound Poisson process, amended by a linear term, representing a constant influx of the insurance premiums.
		Mathematically, the cumulative dividend process is described by an increasing functional which may or may not be continuous with respect to time.
	www.ams.sunysb.edu /papers/papers00.html (4696 words)

	[No title]
		¢ çÿ"çÿ"çÿ"çÿ"çÿ"çÿ" çÿ"çÿ"ª. ó&¤¨Markov Processesª ¨Definition: A stochastic process that has the Markov property is known as a Markov process.
		If state space and time is discrete then process known as Markov chain (see Chapter 2).
		When state space is discrete but time is continuous then known as Markov jump process (see Chapter 3).
	www.ucd.ie /statdept/shanewhelan/sp03lect4-5.ppt (381 words)

	Stability of the trivial solution for linear stochastic differential equations with Poisson white noise
		Two methods are considered for assessing the asymptotic stability of the trivial solution of linear stochastic differential equations driven by Poisson white noise, interpreted as the formal derivative of a compound Poisson process.
		The first method attempts to extend a result for diffusion processes satisfying linear stochastic differential equations to the case of linear equations with Poisson white noise.
		The second method is based on a geometric ergodic theorem for Markov chains providing a criterion for the asymptotic stability of the solution of linear stochastic differential equations with Poisson white noise.
	stacks.iop.org /0305-4470/37/8913 (330 words)

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