On the Goodness-of-Fit Tests for Some Continuous Time Processes

We present a review of several results concerning the construction of the Cramer-von Mises and Kolmogorov-Smirnov type goodness-of-fit tests for continuous time processes. As the models we take a stochastic differential equation with small noise, ergodic diffusion process, Poisson process and self-exciting point processes. For every model we propose the tests which provide the asymptotic size $\alpha$ and discuss the behaviour of the power function under local alternatives. The results of numerical simulations of the tests are presented.Comment: 22 pages, 2 figure

On Compound Poisson Processes Arising in Change-Point Type Statistical Models as Limiting Likelihood Ratios

Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In a previous paper of one of the authors it was established that one of these likelihood ratios, which is an exponential functional of a two-sided Poisson process driven by some parameter, can be approximated (for sufficiently small values of the parameter) by another one, which is an exponential functional of a two-sided Brownian motion. In this paper we consider yet another likelihood ratio, which is the exponent of a two-sided compound Poisson process driven by some parameter. We establish, that similarly to the Poisson type one, the compound Poisson type likelihood ratio can be approximated by the Brownian type one for sufficiently small values of the parameter. We equally discuss the asymptotics for large values of the parameter and illustrate the results by numerical simulations

Optimal entry to an irreversible investment plan with non convex costs

A problem of optimally purchasing electricity at a real-valued spot price (that is, allowing negative prices) has been recently addressed in De Angelis et al. (SIAM J Control Optim 53(3), 1199–1223, 2015). The problem can be considered one of irreversible investment with a cost function which is non convex with respect to the control variable. In this paper we study optimal entry into the investment plan. The optimal entry policy can have an irregular boundary, with a kinked shape

Measurement of D+- and D0 production in deep inelastic scattering using a lifetime tag at HERA

The production of D-+/-- and D-0-mesons has been measured with the ZEUS detector at HERA using an integrated luminosity of 133.6 pb(-1). The measurements cover the kinematic range 5 < Q(2) < 1000 GeV2, 0.02 < y < 0.7, 1.5 < p(T)(D) < 15 GeV and |eta(D)| < 1.6. Combinatorial background to the D-meson signals is reduced by using the ZEUS microvertex detector to reconstruct displaced secondary vertices. Production cross sections are compared with the predictions of next-to-leading-order QCD, which is found to describe the data well. Measurements are extrapolated to the full kinematic phase space in order to obtain the open-charm contribution, F-2(c (c) over bar), to the proton structure function, F-2

The role of ETG modes in JET-ILW pedestals with varying levels of power and fuelling

We present the results of GENE gyrokinetic calculations based on a series of JET-ITER-like-wall (ILW) type I ELMy H-mode discharges operating with similar experimental inputs but at different levels of power and gas fuelling. We show that turbulence due to electron-temperature-gradient (ETGs) modes produces a significant amount of heat flux in four JET-ILW discharges, and, when combined with neoclassical simulations, is able to reproduce the experimental heat flux for the two low gas pulses. The simulations plausibly reproduce the high-gas heat fluxes as well, although power balance analysis is complicated by short ELM cycles. By independently varying the normalised temperature gradients (omega(T)(e)) and normalised density gradients (omega(ne )) around their experimental values, we demonstrate that it is the ratio of these two quantities eta(e) = omega(Te)/omega(ne) that determines the location of the peak in the ETG growth rate and heat flux spectra. The heat flux increases rapidly as eta(e) increases above the experimental point, suggesting that ETGs limit the temperature gradient in these pulses. When quantities are normalised using the minor radius, only increases in omega(Te) produce appreciable increases in the ETG growth rates, as well as the largest increases in turbulent heat flux which follow scalings similar to that of critical balance theory. However, when the heat flux is normalised to the electron gyro-Bohm heat flux using the temperature gradient scale length L-Te, it follows a linear trend in correspondence with previous work by different authors

Spectroscopic camera analysis of the roles of molecularly assisted reaction chains during detachment in JET L-mode plasmas

The roles of the molecularly assisted ionization (MAI), recombination (MAR) and dissociation (MAD) reaction chains with respect to the purely atomic ionization and recombination processes were studied experimentally during detachment in low-confinement mode (L-mode) plasmas in JET with the help of experimentally inferred divertor plasma and neutral conditions, extracted previously from filtered camera observations of deuterium Balmer emission, and the reaction coefficients provided by the ADAS, AMJUEL and H2VIBR atomic and molecular databases. The direct contribution of MAI and MAR in the outer divertor particle balance was found to be inferior to the electron-atom ionization (EAI) and electron-ion recombination (EIR). Near the outer strike point, a strong atom source due to the D+2-driven MAD was, however, observed to correlate with the onset of detachment at outer strike point temperatures of Te,osp = 0.9-2.0 eV via increased plasma-neutral interactions before the increasing dominance of EIR at Te,osp &lt; 0.9 eV, followed by increasing degree of detachment. The analysis was supported by predictions from EDGE2D-EIRENE simulations which were in qualitative agreement with the experimental observations