On the large deviations of a class of modulated additive processes

We prove that the large deviation principle holds for a class of processes inspired by semi-Markov additive processes. For the processes we consider, the sojourn times in the phase process need not be independent and identically distributed. Moreover the state selection process need not be independent of the sojourn times. We assume that the phase process takes values in a finite set and that the order in which elements in the set, called states, are visited is selected stochastically. The sojourn times determine how long the phase process spends in a state once it has been selected. The main tool is a representation formula for the sample paths of the empirical laws of the phase process. Then, based on assumed joint large deviation behavior of the state selection and sojourn processes, we prove that the empirical laws of the phase process satisfy a sample path large deviation principle. From this large deviation principle, the large deviations behavior of a class of modulated additive processes is deduced. As an illustration of the utility of the general results, we provide an alternate proof of results for modulated L´evy processes. As a practical application of the results, we calculate the large deviation rate function for a processes that arises as the International Telecommunications Union’s standardized stochastic model of two-way conversational speech

Large deviations for a damped telegraph process

In this paper we consider a slight generalization of the damped telegraph process in Di Crescenzo and Martinucci (2010). We prove a large deviation principle for this process and an asymptotic result for its level crossing probabilities (as the level goes to infinity). Finally we compare our results with the analogous well-known results for the standard telegraph process

Large deviations for perturbed Gaussian processes and logarithmic asymptotic estimates for some exit probabilities

The main results in this paper concern large deviations for families of non-Gaussian processes obtained as suitable perturbations of continuous centered multivariate Gaussian processes which satisfy a large deviation principle. We present some corollaries and, as a consequence, we obtain logarithmic asymptotic estimates for exit probabilities from suitable halfspaces and quadrants.Comment: 22 page

Moderate deviation estimates for nodal lengths of random spherical harmonics

We prove Moderate Deviation estimates for nodal lengths of random spherical harmonics both on the whole sphere and on shrinking spherical domains. Central Limit Theorems for the latter were recently established in Marinucci et al. (2020) and Todino (2020), respectively. Our proofs are based on the combination of a Moderate Deviation Principle by Schulte and Thäle (2016) for sequences of random variables living in a fixed Wiener chaos with a well-known result based on the concept of exponential equivalenc

Noncentral moderate deviations for time-changed Lévy processes with inverse of stable subordinators

This paper presents some extensions of recent noncentral moderate deviation results. In the first part, the results in [Statist. Probab. Lett. 185, Paper No. 109424, 8 pp. (2022)] are generalized by considering a general Lévy process {S(t) : t ≥ 0} instead of a compound Poisson process. In the second part, it is assumed that {S(t) : t ≥ 0} has bounded variation and is not a subordinator; thus {S(t) : t ≥ 0} can be seen as the difference of two independent nonnull subordinators. In this way, the results in [Mod. Stoch. Theory Appl. 11, 43–61] for Skellam processes are generalized

Sample path large deviations principles for poisson shot noise processes, and applications

This paper concerns sample path large deviations for Poisson shot noise processes, and applications in queueing theory. We first show that, under an exponential tail condition, Poisson shot noise processes satisfy a sample path large deviations principle with respect to the topology of pointwise convergence. Under a stronger superexponential tail condition, we extend this result to the topology of uniform convergence. We also give applications of this result to determining the most likely path to overflow in a single server queue, and to finding tail asymptotics for the queue lengths at priority queues

Heavy metal distribution in a sediment phytoremediation system at pilot scale

The continuous stream of polluted sediments, dredged from harbors and water bodies in order to maintain the navigation, is a common practice, but the fate of these sediments is an issue recognized worldwide. This pilot case study evaluated the application of phytoremediation as sustainable management strategy for the decontamination of polluted dredged marine sediments. The synergic action of different plant species (Paspalum vaginatum; P. vaginatum + Spartium junceum and P. vaginatum + Tamarix gallica) and organic matter (compost) in removing both heavy metals (Cd, Ni, Zn, Pb and Cu) and total petroleum hydrocarbons, and in recovering the nutritive and biological sediment properties were evaluated. In addition to the detection of total metal removal efficiency, the chemical distribution of metals in the sediment phases (exchangeable, manganese and iron oxides, organic matter and residual minerals) was also measured in order to make a more realistic estimation of the phytoremediation efficiency for the sediment decontamination. Finally, a complete picture of the metal flux was obtained by investigating the metal mass-balance in the treated sediments. The results of metal content in the sediment phases showed that metal distribution was not uniform and each metal predominated in different fractions; the solubility of metals in the sediment in the decreasing order was: Cd>Zn>Cu>Pb>Ni. The higher proportion of Ni and Pb in the residual phase can be the reason of the lower translocation of these metals in the plant tissues. On the other hand, Cd, Zn and Cu were the metals most easily translocated in plant tissues, both aboveground and roots, confirming their higher availability for the plants. The results of mass balance indicated that, at the end of the experimentation, a high content of metals were still found in the sediment. The greatest contribution in metal removal was attributed to a phytostabilization process at rhizosphere level followed by gravel and sand absorption. The capacity of rhizophere to precipitate heavy metals, could be considered as an alternative option for reducing the metal availability and, consequently, the toxicity in contaminated sediments

Incidence trends of colorectal cancer in the early 2000s in Italy. Figures from the IMPATTO study on colorectal cancer screening

We utilised the IMPATTO study's archives to describe the 2000-2008 colorectal cancer (CRC) incidence rate trends in Italy, once screening programmes based on the faecal immunochemical test were implemented in different areas. Data on CRCs diagnosed in Italy from 2000 to 2008 in subjects aged 40-79 years were collected by 23 cancer registries. Incidence rate trends were evaluated as a whole and by macro-area (North-Centre and South-Islands), presence of a screening programme, sex, ten-year age class, anatomic site, stage at diagnosis, and pattern of diagnosis (screen-detected, non-screen-detected). The annual percent change (APC) of incidence rate trends, with 95% confidence intervals (95%CI), were computed. The study included 46,857 CRCs diagnosed in subjects aged 40-79 years, of which 2,806 were screendetected. The incidence rates in the North-Centre were higher than in the South and on the Islands. During the study period, screening programmes had been implemented only in the North-Centre and had a significant effect on incidence rates, with an initial sharp increase in incidence, followed by a decrease that started in the 3rd-4th years of screening. These incidence rate trends were exclusively due to modifications in the rates of stage I cases. After screening programmes started, incidence increased in all anatomic sites, particularly in the distal colon. The differential figures introduced by the implementation of screening programmes warrant a continuous surveillance of CRC incidence and mortality trends to monitor the impact of screening at a national level

Decúbito como fator agravante da cefaleia na crise migranosa

Macci JP, Jabarra CP, Teles MC, Ferreira GF, De Souza JA, Moreira Filho PF. Decúbito como fator agravante da cefaleia na crise migranosa. Headache Medicine. 2012;3(4