1 - 10 of 26 articles
We consider the spectral problem for the random Schrödinger operator on the multidimensional lattice torus increasing to the whole of lattice, with an i.i.d. potential (Anderson Hamiltonian). We prove complete Poisson-type limit theorems for the (normalized) eigenvalues and their locations,...
A spatial autoregressive process with two parameters is investigated both in the stable and in the unstable case. It is shown that the limiting distribution of the least squares estimator of these parameters is normal and the rate of convergence is n
3/2 if one of the key parameters equals zero...
We consider the asymptotic behavior of the number of irreducible polynomials over a finite field in arithmetic progressions.
We reduce the construction of a weak solution of the Cauchy problem for a quasilinear parabolic equation to the construction of a solution to a stochastic problem. Namely, we construct a diffusion process that allows us to obtain a probabilistic representation of a weak (in distributional sense)...
We show that the without replacement bootstrap of Booth, Butler and Hall (J. Am. Stat. Assoc.
89, 1282–1289, 1994) provides second order correct approximation to the distribution function of a Studentized U-statistic based on simple random sample drawn without replacement. In order to achieve...
We introduce a new class of dynamic point process models with simple and intuitive dynamics that are based on the Voronoi tessellations generated by the processes. Under broad conditions, these processes prove to be ergodic and produce, on stabilisation, a wide range of clustering patterns. In...
Recently, Philippe et al. (C.R. Acad. Sci. Paris. Ser. I
342, 269–274, 2006; Theory Probab. Appl., 2007, to appear) introduced a new class of time-varying fractionally integrated filters A(d)x
depending on arbitrary given...
A discrete-time financial market model is considered with a sequence of investors whose preferences are described by concave strictly increasing functions defined on the whole real line. Under suitable conditions we prove that, whenever their absolute risk-aversion tends to infinity, the...
The Markov binomial distribution is approximated by the binomial distribution. Estimates of accuracy are obtained for the total variation and local norms. The results include second-order estimates and asymptotically sharp constants.
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