Enlargement of the Wiener filtration by an absolutely continuous random variable via Malliavin’s calculus

Summary. The analytic treatment of problems related to the asymptotic behaviour of random dynamical systems generated by stochastic differential equations suffers from the presence of non-adapted random invariant measures. Semimartingale theory becomes accessible if the underlying Wiener filtration is enlarged by the information carried by the orthogonal projectors on the Oseledets spaces of the (linearized) system. We study the corresponding problem of preservation of the semimartingale property and the validity of a priori inequalities between the norms of stochastic integrals in the enlarged filtration and norms of their quadratic variations in case the random element F enlarging the filtration is real valued and possesses an absolutely continuous law. Applying the tools of Malliavin’s calculus, we give smoothness conditions on F under which the semimartingale property is preserved and a priori martingale inequalities are valid. Received: 12 April 1995 / In revised form: 7 March 1996     

Searching for losers

We investigate the following process: N people select b losers by flipping coins. The 0-party continues until there are less than b losers; then the 1-party has to find the other losers by the same process. The average time for this process is about long₂ N, but this result requires rather advanced methods. Furthermore, the average size of a binary tree associated to this process and the average number of coin flippings are computed. The method used in this article can be used to give asympotical solutions of a special type of bivariate recurrences. © 1993 John Wiley & Sons, Inc.     

Electromagnetic field singularities

An integral transform based method is given for determining information about the locating and properties of singularities of electromagnetic fields associated with axially symmetric radiating sources.     

A STRASSEN LAW OF THE ITERATED LOGARITHM FOR PROCESSES WITH INDEPENDENT INCREMENT

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Alloying by high dose ion implantation of iron into magnesium and aluminium

Alloys of the systems Fe–Al (mixable over the whole concentration range) and Fe–Mg (insoluble with each other) were produced by implantation of Fe ions into Al and Mg, respectively. The implantation energy was 200 keV and the ion doses ranged from 1 × 10₁₄ to 9 × 10₁₇cm^-2The obtained implantation profiles were determined by Auger electron spectroscopy depth profiling. Maximum iron concentrations reached were up to 60 at.% for implantation into Al and 94 at.% for implantation into Mg. Phase analysis of the implanted layers was performed by conversion electron Mössbauer spectroscopy and X‐ray diffraction. For implantation into Mg, two different kinds of Mössbauer spectra were obtained: at low doses paramagnetic doublets indicating at least two different iron sites and at high doses a dominant ferromagnetic six‐line‐pattern with a small paramagnetic fraction. The X‐ray diffraction pattern concluded that in the latter case a dilated αiron lattice is formed. For implantation into Al, the Mössbauer spectra were doublet structures very similar to those obtained at amorphous Fe–Al alloys produced by rapid quenching methods. They also indicated at least two different main iron environments. For the highest implanted sample a ferromagnetic six‐line‐pattern with magnetic field values close to those of Fe₃Al appeared.     

State of and prospects for XeF(C−A) optically pumped lasers

Experimental and theoretical results are presented on an XeF(C?A) blue-green laser driven by 5-kJ energy. The laser was pumped by a ferrite-induced discharge of 90 cm in length. The output energy of 0.22 J was obtained with a plane-parallel resonator. A program to simulate laser operation has been developed. Numerical results for a wide range of conditions are compared with experiments performed by us and by other authors. It is found that intracavity refractive losses limit laser operation for XeF pressures above 3 torr. The laser efficiency strongly depends on the discharge-to-cavity length ratio. Possible ways to increase the laser power and efficiency are discussed.