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Simple Monte Carlo integration with respect to Bernoulli convolutions

David M. Gómez, Pablo Dartnell (2012)

Applications of Mathematics

We apply a Markov chain Monte Carlo method to approximate the integral of a continuous function with respect to the asymmetric Bernoulli convolution and, in particular, with respect to a binomial measure. This method---inspired by a cognitive model of memory decay---is extremely easy to implement, because it samples only Bernoulli random variables and combines them in a simple way so as to obtain a sequence of empirical measures converging almost surely to the Bernoulli convolution. We give explicit...

Some properties of superprocesses under a stochastic flow

Kijung Lee, Carl Mueller, Jie Xiong (2009)

Annales de l'I.H.P. Probabilités et statistiques

For a superprocess under a stochastic flow in one dimension, we prove that it has a density with respect to the Lebesgue measure. A stochastic partial differential equation is derived for the density. The regularity of the solution is then proved by using Krylov’s Lp-theory for linear SPDE.

Strong and weak solutions to stochastic inclusions

Michał Kisielewicz (1995)

Banach Center Publications

Existence of strong and weak solutions to stochastic inclusions x t - x s ∈ ∫ s t F τ ( x τ ) d τ + ∫ s t G τ ( x τ ) d w τ + ∫ s t ∫ ℝ n H τ , z ( x τ ) q ( d τ , d z ) and x t - x s ∈ ∫ s t F τ ( x τ ) d τ + ∫ s t G τ ( x τ ) d w τ + ∫ s t ∫ | z | ≤ 1 H τ , z ( x τ ) q ( d τ , d z ) + ∫ s t ∫ | z | > 1 H τ , z ( x τ ) p ( d τ , d z ) , where p and q are certain random measures, is considered.

The distribution of eigenvalues of randomized permutation matrices

Joseph Najnudel, Ashkan Nikeghbali (2013)

Annales de l’institut Fourier

In this article we study in detail a family of random matrix ensembles which are obtained from random permutations matrices (chosen at random according to the Ewens measure of parameter θ > 0 ) by replacing the entries equal to one by more general non-vanishing complex random variables. For these ensembles, in contrast with more classical models as the Gaussian Unitary Ensemble, or the Circular Unitary Ensemble, the eigenvalues can be very explicitly computed by using the cycle structure of the permutations....

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