Asymptotic behavior of parameter estimators of a multivariate discontinuous density

We study the asymptotic behavior of Bayesian and maximum likelihood estimators of the parameter when the density function f(x, ) for each fixed x has discontinuities in on some surface.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 74, pp. 83–107, 1977.     

Elliptic semiplanes and group divisible designs with orthogonal resolutions

In this paper we prove that there exists an elliptic semiplaneS(v, k, m) withk –m 2 if and only if there exists a group divisible design GDD _k ((k –m)(k – 1);k –m; 0, 1) withm pairwise orthogonal resolutions. As an example of this theorem, we construct an elliptic semiplaneW(45, 7, 3) and show thatW is isomorphic to the elliptic semiplaneS(45, 7, 3) given by R. D. Baker.     

Finiteness of Ricci flatN=2 supersymmetric σ-models

We study the ultraviolet behavior of two dimensional supersymmetric non-linear -models with target space an arbitrary Kähler manifoldM, so that the models areN=2 supersymmetric. We point out that these models have an additional fermionic axial symmetry if and only if the metric onM is Ricci flat. We show that the preservation of this symmetry in perturbation theory implies that both bare and renormalized metrics onM are Ricci flat. Combining this result with the constraint ofN=2 supersymmetry requiring that all counter-terms to the metric beyond one-loop order be cohomologically trivial, we argue thatN=2 models defined on Ricci flat Kähler manifolds are on-shell ultraviolet finite to all orders of perturbation theory.     

Periodic behavior of the stochastic Brusselator in the mean-field limit

Summary We prove a propagation of chaos result for the mean-field limit of a model for a trimolecular chemical reaction called Brusselator. Then we show that the pair of nonlinear (i.e. law-dependent) stochastic differential equations describing the evolution of the concentration of the molecules at a given site in the mean field limit has a solution with a periodic law (in t). Finally we identify the limit and establish a central limit theorem for the periodic law in the case where the noise tends to zero.Part of this work was performed while on leave at the Department of Mathematics and Statistics, Carleton University, Ottawa, Canada and supported by NSERC operating grants of M. Csörgö and D. Dawson     

Renewal theorem for a class of stationary sequences

Summary A renewal theorem is obtained for stationary sequences of the form _n=(...,X _n-1,X _n,X _n+1...), whereX _n, , are i.i.d. r.v.s. valued in a Polish space. This class of processes is sufficiently broad to encompass functionals of recurrent Markov chains, functionals of stationary Gaussian processes, and functionals of one-dimensional Gibbs states. The theorem is proved by a new coupling construction.Research supported by the National Science Foundation     

How large can a hereditarily separable or hereditarily Lindelöf space be?

The main result of this paper is that ifV satisfies GCH andω ₁<λ<μ are arbitrary regular cardinals, then in some cardinal preserving forcing extensionW ofV we have λ^<λ=λ=2 ^N 0,μ=2 ^λ and there are a hereditarily separableX ?2 ^λ with |X|= \(2^{\aleph _0 } \) =μ and a hereditarily LindelöfY ?2 ^μ withw(Y)= \(2^{2^\aleph 0} \) =μ. So far similar results have only been obtained under the assumption of CH.     

Observables on hypergraphs

Observables on hypergraphs are described by event-valued measures. We first distinguish between finitely additive observables and countably additive ones. We then study the spectrum, compatibility, and functions of observables. Next a relationship between observables and certain functionals on the set of measures M(H) of a hypergraph H is established. We characterize hypergraphs for which every linear functional on M(H) is determined by an observable. We define the concept of an effect and show that observables are related to effect-valued measures. Finally, we define operational transformations from M(H) to itself and show that they can be described as a certain combination of effects.On leave from University of Berne, Institute of Mathematical Statistics, Sidlerstrasse 5, CH-3012 Berne, Switzerland.