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1	On the role of non-uniform smoothness parameters and the probabilistic method in applications of the Stein-Chen Method Weinberg, Graham Victor Unknown Date (has links) (PDF) The purpose of the research presented here is twofold. The first component explores the probabilistic interpretation of Stein’s method, as introduced in Barbour (1988). This is done in the setting of random variable approximations. This probabilistic method, where the Stein equation is interpreted in terms of the generator of an underlying birth and death process having equilibrium distribution equal to that of the approximant, provides a natural explanation of why Stein’s method works. An open problem has been to use this generator approach to obtain bounds on the differences of the solution to the Stein equation. Uniform bounds on these differences produce Stein “magic” factors, which control the bounds. With the choice of unit per capita death rate for the birth and death process, we are able to produce a result giving a new Stein factor bound, which applies to a selection of distributions. The proof is via a probabilistic approach, and we also include a probabilistic proof of a Stein factor bound from Barbour, Holst and Janson (1992). These results generalise the work of Xia (1999), which applies to the Poisson distribution with unit per capita death rate. (For complete abstract open document)
2	A Limit Theorem in Cryptography. Lynch, Kevin 16 August 2005 (has links) (PDF) Cryptography is the study of encryptying and decrypting messages and deciphering encrypted messages when the code is unknown. We consider Λπ(Δx, Δy) which is a count of how many ways a permutation satisfies a certain property. According to Hawkes and O'Connor, the distribution of Λπ(Δx, Δy) tends to a Poisson distribution with parameter ½ as m → ∞ for all Δx,Δy ∈ (Z/qZ)m - 0. We give a proof of this theorem using the Stein-Chen method: As qm approaches infinity, the distribution of Λπ(Δx, Δy) is approximately Poisson with parameter ½. Error bounds for this approximation are provided. Cryptography Stein-Chen Method Poisson Approximation Cryptanalysis Error Bound Coupling Method Even Word Multiple of Three Word Applied Mathematics Physical Sciences and Mathematics
3	Some contributions in probability and statistics of extremes. Kratz, Marie 15 November 2005 (has links) (PDF) Part I - Level crossings and other level functionals.<br />Part II - Some contributions in statistics of extremes and in statistical mechanics. [MATH] Mathematics autoregressive processes chaos decomposition CLT crossings empirical process exceedances extremes Gaussian fileds Gaussian processes heavy tails Hermite polynomials level curve level functionals linear programming maxima moving average processes order statistics parameter estimation Poisson convergence Poisson processes qq-plot random spin systems rate of convergence regular variation sojourn time spectral moment Stein-Chen method time series analysis

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