The theme of providing predictable criteria for absolute continuity and for mutual singularity of two density processes on a filtered probability space is extensively studied, e.g., in the monograph by J. Jacod and A. N. Shiryaev [JS]. While the issue of absolute continuity is settled there in full generality, for the issue of mutual singularity one technical difficulty remained open ([JS], p210): "We do not know whether it is possible to derive a predictable criterion (necessary and sufficient condition) for "P'T..." (expression not representable in this abstract). It turns out that to this question raised in [JS] which we also chose as the title of this note, there are two answers: on the negative side we give an easy example, showing that in general the answer is no, even when we use a rather wide interpretation of the concept of "predictable criterion". The difficulty comes from the fact that the density process of a probability measure P with respect to another measure P' may suddenly jump to zero. On the positive side we can characterize the set, where P' becomes singular with respect to P - provided this does not happen in a sudden but rather in a continuous way - as the set where the Hellinger process diverges, which certainly is a "predictable criterion". This theorem extends results in the book of J. Jacod and A. N. Shiryaev [JS]. (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

This report is mainly based on the paper "Optimal multiple stopping and valuation of swing options" by R. Carmona and N. Touzi (1). Here the authors model and solve optimal stopping problems with more than one exercise time. The existence of optimal stopping times is firstly proved and they then construct the value function of American put options with multiple exercises in the case of the Black-Scholes model, characterizing the exercise boundaries of the perpetual case. Finally, they extend the analysis to the swing contracts with infinitely many exercise rights. In this report, we concentrate on explaining their rigorous mathematical analysis in detail, especially for the valuation of the perpetual American put options with single exercise and two exercise rights, and the characteristics of the exercise boundaries of the multiple stopping case. These results are presented as theorems in Chapter 2 and Chapter 3. / text

No description available.

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 1989. / Includes bibliographical references (p. 82-83).

Small failures should only disrupt a small part of a network. One wayto do this is by marking the surrounding area as untrustworthy ---circumscribing the failure. This can be done with a distributedalgorithm using hierarchical clustering and neighbor relations, andthe resulting circumscription is near-optimal for convex failures.

A perda de energia de íons na matéria é um tópico importante não apenas devido à sua direta aplicação nas técnicas de análises de materiais mas também na compreensão da interação íon-átomo. O conhecimento preciso do poder de freamento de íons pesados a baixas energias é cada vez mais necessário em ciências dos materiais assim como na física nuclear básica, como por exemplo, no Método da Atenuação do Deslocamento Doppler (DSAM, na sigla em inglês). Nessa técnica, o conhecimento do poder de freamento é utilizado para determinar uma referência temporal para o decaimento nuclear enquanto em recuo em um substrato, tipicamente Au ou Pb. No entanto, o freamento de íons pesados em sólidos é ainda pouco compreendido principalmente com respeito a região de baixas energias devido às dificuldades adicionais que surgem da complicada dependência entre o estado de carga do projétil e sua velocidade instantânea no freador. Como modelos teóricos não são capazes de fornecer fornecer previsões quantitativas confiáveis, os principais modelos utilizados atualmente são de natureza semiempírica. O principal objetivo desse trabalho se concentra na obtenção de novos dados experimentais na região de energia de 100-500 keV/u.m.a., para o freamento de Ti, V, Cr, Co, Ni em Au e Ge e de Ti e Cr em Pb. Os dados experimentais com os íons de Ti, V e Cr foram obtidos utilizando a técnica de espalhamento elástico, na qual o feixe primário é espalhado por átomos de um fino alvo ( 100µg/cm²). O feixe primário espalhado produz átomos do alvo com baixas energia em recuo numa determinada direção. Os experimentais com íons de Co e Ni foram obtidos utilizando um arranjo de ToF-E (Time of Flight - Energy ) que permite a medida do freamento ao longo de uma região contínua de energia. Nesta técnica, para a produção de um feixe com ampla distribuição em energia, o feixe primário monoenergético é espalhado por substrato de Au. Os dados experimentais foram comparados com as previsões da Teoria Binária (TB) e Aproximação de Convolução Unitária (ACU) e dos modelos semiempíricos de Ziegler, Biersack e Littmark (ZBL) e de Northcliffe e Schilling (NS). Apesar dos modelos descreverem razoavelvii mente bem os freamentos de Ti, V e Cr em Au, os dados experimentais para o freamento de Ni em Au, por exemplo, chegam a ser 2 vezes maiores que as previsões de ZBL. / The energy loss of ions in materials is an important issue not only because of its direct applications on material analysis techniques, but also for the understanding of the interactions. Accurate knowledge of heavy ion stopping power at low energies is necessary in materials science as well as in basic physics, e. g. in the Doppler Shift Attenuation Method (DSAM). In this technique the knowledge of stopping power is used to determine the timescale for the decaying nuclei while slowing down in a heavy substrate, usually Au or Pb. Nevertheless, the stopping power of solids for heavy ions is still poorly known. Regarding to low energies, this is especially true due to additional difficulties arising from a complicated dependence of the projectile charge state and its istantaneous velocity in the medium. Since theoretical models are unable to produce reliable quantitative predictions, most models currently in use are of semiempirical nature. The main aim of this work is to present new experimental data in the energy range 100-500 keV/u for Ti, V, Cr, Co and Ni ions slowing down in Au and Ge, and Ti and Cr ions slowing down in Pb. Experimental data for Ti, V, Cr ions were obtained using the elastic recoil technique, where a primary beam is scattered by heavy ions from a thin target (100µg/cm²). The scattered primary beam produces recoiling atoms of the target at low energies and at a given direction, where it is placed the stoppers. Experimental data for Co and Ni ions were obtained using a ToF-E apparatus (Time of Flight - Energy detection system) which allows measuring stopping over a continuous energy range. To produce a beam of Co, for instance, with broad energy range its monoenergetic beam is scattered away by a Au substract. Our experimental data were compared to TB and UCA theories and ZBL and NS semiempical models. Although there is an overall agreement between experiment and theory for Ti, V and Cr ions, the experimental stopping power for Ni in Au, for instance, is about 2 times greater than the ZBL prediction.

We consider transformations of a given random walk on a countable group determined by Markov stopping times. We prove that these transformations preserve the Poisson boundary. Moreover, under some mild conditions, the asymptotic entropy (resp., rate of escape) of the transformed random walks is equal to the asymptotic entropy (resp., rate of escape) of the original random walk multiplied by the expectation of the corresponding stopping time. This is an analogue of the well-known Abramov's formula from ergodic theory.

No description available.

P300 spellers provide a noninvasive method of communication for people who may not be able to use other communication aids due to severe neuromuscular disabilities. However, P300 spellers rely on event-related potentials (ERPs) which often have low signal-to-noise ratios (SNRs). In order to improve detection of the ERPs, P300 spellers typically collect multiple measurements of the electroencephalography (EEG) response for each character. The amount of collected data can affect both the accuracy and the communication rate of the speller system. The goal of the present study was to develop an algorithm that would automatically determine the necessary amount of data to collect during operation. Dynamic data collection was controlled by a threshold on the probabilities that each possible character was the target character, and these probabilities were continually updated with each additional measurement. This Bayesian technique differs from other dynamic data collection techniques by relying on a participant-independent, probability-based metric as the stopping criterion. The accuracy and communication rate for dynamic and static data collection in P300 spellers were compared for 26 users. Dynamic data collection resulted in a significant increase in accuracy and communication rate.

P300 spellers provide a noninvasive method of communication for people who may not be able to use other communication aids due to severe neuromuscular disabilities. However, P300 spellers rely on event-related potentials (ERPs) which often have low signal-to-noise ratios (SNRs). In order to improve detection of the ERPs, P300 spellers typically collect multiple measurements of the electroencephalography (EEG) response for each character. The amount of collected data can affect both the accuracy and the communication rate of the speller system. The goal of the present study was to develop an algorithm that would automatically determine the necessary amount of data to collect during operation. Dynamic data collection was controlled by a threshold on the probabilities that each possible character was the target character, and these probabilities were continually updated with each additional measurement. This Bayesian technique differs from other dynamic data collection techniques by relying on a participant-independent, probability-based metric as the stopping criterion. The accuracy and communication rate for dynamic and static data collection in P300 spellers were compared for 26 users. Dynamic data collection resulted in a significant increase in accuracy and communication rate.