منابع مشابه
Poisson superposition processes
Superposition is a mapping on point configurations that sends the n-tuple (x1, . . . , xn) ∈ X into the n-point configuration {x1, . . . , xn} ⊂ X , counted with multiplicity. It is an additive set operation such the superposition of a k-point configuration in X is a kn-point configuration in X . A Poisson superposition process is the superposition in X of a Poisson process in the space of fini...
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The characteristic independence property of Poisson point processes gives an intuitive way to explain why a sequence of point processes becoming less and less repulsive can converge to a Poisson point process. The aim of this paper is to show this convergence for sequences built by superposing repulsive point processes. We use Papangelou intensities and Stein’s method to prove this result with ...
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Here a is a positive semidefinite symmetric matrix for each t and x, and b is a d vector for each t and x. There are various ways of describing exactly what we mean by a diffusion process corresponding to the specified set of coefficients. We shall adopt the following approach. Let Q be the space of Rd valued continuous functions on [0, cc). The value of a function ow = x( ) in Q at time t will...
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Although the study of weak convergence of superpositions of point processes to the Poisson process dates back to the work of Grigelionis in 1963, it was only recently that Schuhmacher [Stochastic Process. Appl. 115 (2005) 1819–1837] obtained error bounds for the weak convergence. Schuhmacher considered dependent superposition, truncated the individual point processes to 0–1 point processes and ...
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1980
ISSN: 0025-5645
DOI: 10.2969/jmsj/03240671