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Verjetnostni račun in statistika

Slučajne mere subordinatorskega tipa : [slučajno vzorčenje iz Poissonovih procesov]. Del 1

Points of a Poisson point process in an abstract space are being sampled randomly. A point is chosen with probability proportional to its size where the size is defined as an arbitrary strictly positive function. The sizes of points chosen form a sequence of random variables whose distribution is described.These results are used to explain vhy in cases of "gamma" or "stable" one-sided Lévy processes the relative sizes of jumps can be represented by the random allocation model. A further application is to sampling of excursions of a Markov process away form a recurrent point, in particular for Brownian motion or Bessel processes for which the inverse local time is a stable one-sided Lévy proces. One of the theorems proved generalises the arcsine law for the time Brownian motion spends positive.

Points of a Poisson point process in an abstract space are being sampled randomly.