An optimal transportation approach for assessing almost stochastic order

When stochastic dominance $F\leq_{st}G$ does not hold, we can improve agreement to stochastic order by suitably trimming both distributions. In this work we consider the $L_2-$Wasserstein distance, $\mathcal W_2$, to stochastic order of these trimmed versions. Our characterization for that distance naturally leads to consider a $\mathcal W_2$-based index of disagreement with stochastic order, $\varepsilon_{\mathcal W_2}(F,G)$. We provide asymptotic results allowing to test $H_0: \varepsilon_{\mathcal W_2}(F,G)\geq \varepsilon_0$ vs $H_a: \varepsilon_{\mathcal W_2}(F,G)<\varepsilon_0$, that, under rejection, would give statistical guarantee of almost stochastic dominance. We include a simulation study showing a good performance of the index under the normal model

Regression-based seasonal unit root tests

The contribution of this paper is three-fold. Firstly, a characterisation theorem of the sub-hypotheses comprising the seasonal unit root hypothesis is presented which provides a precise formulation of the alternative hypotheses against which regression-based seasonal unit root tests test. Secondly, it proposes regressionbased tests for the seasonal unit root hypothesis which allow a general seasonal aspect for the data and are similar both exactly and asymptotically with respect to initial values and seasonal drift parameters. Thirdly, limiting distribution theory is given for these statistics where, in contrast to previous papers in the literature, in doing so it is not assumed that unit roots hold at all of the zero and seasonal frequencies. This is shown to alter the large sample null distribution theory for regression t-statistics for unit roots at the complex frequencies, but interestingly to not affect the limiting null distributions of the regression t-statistics for unit roots at the zero and Nyquist frequencies and regression Fstatistics for unit roots at the complex frequencies. Our results therefore have important implications for how tests of the seasonal unit root hypothesis should be conducted in practice. Associated simulation evidence on the size and power properties of the statistics presented in this paper is given which is consonant with the predictions from the large sample theory.Seasonal unit root tests; seasonal drifts; characterisation theorem

Sub-Nanosecond Switching of HV SiC MOS Transistors for Impact Ionisation Triggering

Pulse generators with multi kV/kA pulses are necessary for the particle accelerator environment for beam transfer magnets. Traditionally these generators are using thyratrons - until recently the only switches capable of switching such pulses within tens of ns. There is a strong demand to replace thyratrons with semiconductor switches to avoid their future obsolescence. Very promising candidates are components from the family of fast ionization dynistors triggered by impact ionization. Their sub-nanosecond switching time and extreme current densities can provide performances superior to that of thyratrons. Recent investigations showed that impact ionization triggering is feasible also in cheap industrial thyristors. The main issue is the generation of triggering pulses with slew rates in the multi kV/ns region and with the required output current for charging the parasitic capacitance of the thyristor. We present an approach of generating > 1 kV/ns pulses by ultra-boosted gate driving of HV SiC MOS transistors. We found that the MOS lifetime under these extreme triggering conditions can still reach more than 10⁸ pulses, enough for kicker generator applications

Ultra-Fast Generator for Impact Ionization Triggering

Impact ionization triggering can be successfully applied to standard thyristors, thus boosting their dI/dt capability by up to 1000x. This groundbreaking triggering requires applying significant overvoltage on the anode-cathode of thyristor with a slew rate > 1kV/ns. Compact pulse generators based on commercial off-the-shelf (COTS) components would allow the spread of this technology into numerous applications, including fast kicker generators for particle accelerators. In our approach, the beginning of the triggering chain is a HV SiC MOS with an ultra-fast super-boosting gate driver. The super boosting of a 1.7kV rated SiC MOS allows to reduce the MOS rise time by a factor of > 25 (datasheet tr = §I{20}{ns} vs. measured tr 1kV/ns and an amplitude > 1kV. Additional boosting is obtained by a Marx generator with GaAs diodes, reaching an output voltage slew rate > 11kV/ns. The final stage will be a Marx generator with medium size thyristors triggered in impact ionization mode with sufficient voltage and current rating necessary for the triggering of a big thyristor. This paper presents the impact ionization triggering of a small size thyristor