Leaving us with fond memories,smiles, SMILES and,alas, tears: a tribute to David Weininger, 1952–2016

David Weininger’s career, accomplishments, genius, and friendship are warmly remembered by several of his colleagues, friends, and admirers.     

Saturation Effects and the Colored Pump Noise in a Dye Laser

We investigate the statistical properties of two single-mode dye-laser models-the colored-loss-noise model and the colored-gain-noise model. Analytic expressions of the probability,the mean and the variance of the steady-state laser intensity are obtained through the unified expansion theory [Phys. Rev. A43 (1991) 700]. By comparison we find that when the cavity decay rate for the electric field is large and the pump parameter a₀ is small, the differences of the results of the two laser models are small. Otherwise, the differences are large. And the correlation time of the noise has very obvious influence on the results of the two models.     

Paolo Pizzetti: The forgotten originator of triangle comparison geometry

The theorem comparing the angles of two geodesic triangles with the same side lengths lying on surfaces with different curvatures, commonly attributed for the two-dimensional case to A.D. Alexandrov (1948) and for the n-dimensional Riemannian case to V.A. Toponogov (1959), goes back, for the two-dimensional case, to Paolo Pizzetti (1907b). Besides suggesting a correction of the historical narrative regarding the development of comparison geometry, the present note also mentions possible reasons for the oversight.     

A strong convergence to the Rosenblatt process

We give a strong approximation of Rosenblatt process via transport processes and we give the rate of convergence.     

Large scale behavior of wavelet coefficients of non-linear subordinated processes with long memory

We study the asymptotic behavior of wavelet coefficients of random processes with long memory. These processes may be stationary or not and are obtained as the output of non-linear filter with Gaussian input. The wavelet coefficients that appear in the limit are random, typically non-Gaussian and belong to a Wiener chaos. They can be interpreted as wavelet coefficients of a generalized self-similar process.     

Besov regularity for the indefinite Skorohod integral with respect to the fractional Brownian motion: The singular case

Using the techniques of the Malliavin calculus and the properties of Gaussian processes, we prove that the paths of the indefinite Skorohod integral with respect to the fractional Brownian motion (fBm) with Hurst parameter less than 1/2 belongs to the Besov space B p , X H , for any p >(1/ H ).