We present a simple proof for bounding the smallest eigenvalue of the empirical covariance in a causal Gaussian process. Along the way, we establish a one-sided tail inequality for Gaussian quadratic ...forms using a causal decomposition. Our proof only uses elementary facts about the Gaussian distribution and the union bound. We conclude with an example in which we provide a performance guarantee for least squares identification of a vector autoregression.
Aims to give to the reader the tools necessary to apply semi-Markov processes in real-life problems. The book is self-contained and, starting from a low level of probability concepts, gradually ...brings the reader to a deep knowledge of semi-Markov processes. Presents homogeneous and non-homogeneous semi-Markov processes, as well as Markov and semi-Markov rewards processes. The concepts are fundamental for many applications, but they are not as thoroughly presented in other books on the subject as they are here.
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•Possible reactive species formed in various AOPs were summarized.•Formation mechanisms and influencing factors of reactive species were analyzed.•Various methods for identifying ...reactive species formed in AOPs were introduced.•Reaction mechanisms of different reactive species with pollutants were discussed.
The formation, identification and reaction mechanism of reactive species in various advanced oxidation processes (AOPs) are crucial for understanding the principles of AOPs and the degradation mechanism of recalcitrant organic contaminants because reactive species are responsible for the degradation of organic contaminants in AOPs. In this review, the possible reactive species generated in various AOPs (such as Fenton oxidation, photochemical oxidation, electrochemical oxidation, ozonation, gamma ray/electron beam radiation, persulfate-based oxidation, wet air oxidation and ultrasonic oxidation), were systematically analyzed and summarized, including hydroxyl radicals (HO), hydrogen radical (H), hydrated electron (eaq−), sulfate radicals (SO4−), peroxymonosulfate radicals (SO5−), superoxide radicals (O2−), singlet oxygen (1O2) and hydroperoxy radicals (HO2). The factors that influence the formation of reactive species were discussed, mainly including pH, inorganic anions and dissolved organic matter. The main identification methods, such as electron spin resonance (ESR), electron paramagnetic electron (EPR), high performance liquid chromatography (HPLC), transient absorption spectrum, quenching experiments and kinetic analysis, were introduced, and the reaction mechanism of reactive species with organic contaminants were discussed. Finally, concluding remarks and perspectives were proposed. This review paper will provide an insight into the formation, identification and reaction mechanism of reactive species in AOPs, which is helpful for reader to better understand the degradation mechanism of recalcitrant organic contaminants in various AOPs.
Pickands constants play a crucial role in the asymptotic theory of Gaussian processes. They are commonly defined as the limits of a sequence of expectations involving fractional Brownian motions and, ...as such, their exact value is often unknown. Recently, Dieker and Yakir (Bernoulli,
20
(3), 1600–1619,
2014
) derived a novel representation of Pickands constant as a simple expected value that does not involve a limit operation. In this paper we show that the notion of Pickands constants and their corresponding Dieker–Yakir representations can be extended to a large class of stochastic processes, including general Gaussian and Lévy processes. We furthermore develop a link to extreme value theory and show that Pickands-type constants coincide with certain constants arising in the study of max-stable processes with mixed moving maxima representations.
The Public Opinion Survey of Human Attributes - Stuttering (POSHA-S, St. Louis, 2013) was developed as a standard measure of public attitudes about people who stutter. As with any survey-based ...methods, threats to validity may occur because of social desirability bias. Using computer mouse-tracking, we were interested in observing changes in cognition that are manifested in intentionality through action by evaluating underlying cognitive processes that drive social judgments of people who stutter.
Twenty-two women, 1 non-binary person, and 47 men reported using a computer mouse to complete an online, remote, and modified version of the POSHA-S. Responses were categorized as correct/helpful or incorrect/unhelpful relative to each component of the POSHA-S and were used as measures of explicit cognitive processes. Computer-mouse trajectory metrics, including area under the curve (AUC) and reaction time (RT), were used to measure implicit cognitive processes.
Although participants’ explicit responses were significantly more likely to be correct/helpful than incorrect/unhelpful, with endorsement of correct/helpful prompts 77 % of the time, participants also endorsed incorrect/unhelpful prompts more than half (i.e., 52 %) of the time. Familiarity with people who stutter was associated with disagreeing with incorrect/unhelpful prompts. As indicated by greater AUC, participants exhibited significantly more implicit cognitive processes indicating competition when responding “disagree” compared to “agree”, regardless of whether the prompts were correct/helpful or incorrect/unhelpful. Similarly, participants took significantly longer to respond to prompts with "disagree" rather than "agree".
The findings of this study offer evidence of participants reporting cognitive processes that are overall more correct/helpful than incorrect/unhelpful, in their explicit responses to the dichotomous response tasks of the POSHA-S. However, these findings are tempered by evidence of a tendency to agree with statements in the measure and suggest the need for further research to increase understanding of how to measure and improve explicit and implicit cognitive processes related to people who stutter.
•Mouse-tracking was used to measure stuttering-related explicit and implicit cognitive processes.•Participants endorsed helpful/correct prompts 77 % of the time.•Participants endorsed unhelpful/incorrect prompts 52 % of the time.•Greater uncertainty was apparent when participants disagreed with statements.
Non-Gaussian processes of Ornstein-Uhlenbeck (OU) type offer the possibility of capturing important distributional deviations from Gaussianity and for flexible modelling of dependence structures. ...This paper develops this potential, drawing on and extending powerful results from probability theory for applications in statistical analysis. Their power is illustrated by a sustained application of OU processes within the context of finance and econometrics. We construct continuous time stochastic volatility models for financial assets where the volatility processes are superpositions of positive OU processes, and we study these models in relation to financial data and theory.
A continuous-time random walk is a simple random walk subordinated to a renewal process used in physics to model anomalous diffusion. In this paper we show that, when the time between renewals has ...infinite mean, the scaling limit is an operator Lévy motion subordinated to the hitting time process of a classical stable subordinator. Density functions for the limit process solve a fractional Cauchy problem, the generalization of a fractional partial differential equation for Hamiltonian chaos. We also establish a functional limit theorem for random walks with jumps in the strict generalized domain of attraction of a full operator stable law, which is of some independent interest.
A p-jump process is a piecewise deterministic Markov process with multiplicative jumps by a factor of p. We prove a limit theorem for such processes on the unit interval. Via duality with respect to ...probability generating functions, we deduce limiting results for the survival probabilities of time-homogeneous branching processes with arbitrary offspring distributions, underlying binomial disasters. Extending this method, we obtain corresponding results for time-inhomogeneous birth–death processes underlying time-dependent binomial disasters and continuous state branching processes with p-jumps.
Integer-valued time series, seen as a collection of observations measured sequentially over time, have been studied with deep notoriety in recent years, with applications and new proposals of ...autoregressive models that broaden the field of study. This work proposes a new mixed integer-valued first-order autoregressive model with Poisson innovations, denoted POMINAR(1), mixing two operators known as binomial thinning and Poisson thinning. The proposed process presents some advantages in relation to the most common Poisson innovation processes: (1) this new process allows to capture structural changes in the data; (2) if there are no structural changes, the most common processes with Poisson innovations are particular cases of POMINAR(1). Another important contribution of this work is the establishment of the POMINAR(1) theoretical results, such as the marginal expectation, marginal variance, conditional expectation, conditional variance, transition probabilities. Moreover, the Conditional Maximum Likelihood (CML) and Yule-Walker (YW) estimators for the process parameters are studied. We also present three techniques for one-step-ahead forecasting, the nearest integer of the conditional expectation, conditional median and mode. A simulation study of the forecasting procedures, considering the two estimators, CML and YW methods, is performed, and prediction intervals are presented. Finally, we show an application of the proposed process to a real dataset, referred here as larceny data, including a residual analysis.
Hoping for Hope Gautam, Vinayshil
Abhigyan (New Delhi),
12/2021, Letnik:
39, Številka:
3
Journal Article
Recenzirano
Odprti dostop
The response to call for contributions to the special issue was overwhelming. It was obvious that no contribution would be accepted without the usual two-tier blind r eview. The numbers were so large ...that even with one special issue being printed (which was done in the last quarter) there remained a set of more papers which merited publication. The referees in certain cases had asked for a review and made some recommendations about it. The authors were very receptive and at least one of them revised it twice. We received contributions in different perspectives about the pandemic both geographically and thematically. Illustratively, papers from Nigeria had a thematic focus on organisation development and made in-depth explorations of some sectors. There were others from different parts of India which looked at the learning processes and related areas. A particular reference can be made to an exploration which this number carries on the unorganised sector. All in all, as is evident from the foregoing, a sequel to the special issue, in its own right, became an obvious way forward.
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