Tail distribution estimates of the mixed-fractional CEV model

The aim of this paper is to study the tail distribution of the CEV model driven by Brownian motion and fractional Brownian motion. Based on the techniques of Malliavin calculus and a result established recently in [<a href="#1">1</a>], we obtain an explicit estimate for tail distributions.

Branching processes with immigration in atypical random environment

Motivated by a seminal paper of Kesten et al. (Ann. Probab., 3(1), 1–31, 1975) we consider a branching process with a conditional geometric offspring distribution with i.i.d. random environmental parameters An, n ≥ 1 and with one immigrant in each generation. In contrast to above mentioned paper we assume that the environment is long-tailed, that is that the distribution F of $\xi _{n}:=\log ((1-A_{n})/A_{n})$ ξ n : = log ( ( 1 − A n ) / A n ) is long-tailed. We prove that although the offspring distribution is light-tailed, the environment itself can produce extremely heavy tails of the distribution of the population size in the n th generation which becomes even heavier with increase of n. More precisely, we prove that, for all n, the distribution tail $\mathbb {P}(Z_{n} \ge m)$ ℙ ( Z n ≥ m ) of the n th population size Zn is asymptotically equivalent to $n\overline F(\log m)$ n F ¯ ( log m ) as m grows. In this way we generalise Bhattacharya and Palmowski (Stat. Probab. Lett., 154, 108550, 2019) who proved this result in the case n = 1 for regularly varying environment F with parameter α > 1. Further, for a subcritical branching process with subexponentially distributed ξn, we provide the asymptotics for the distribution tail $\mathbb {P}(Z_{n}>m)$ ℙ ( Z n > m ) which are valid uniformly for all n, and also for the stationary tail distribution. Then we establish the “principle of a single atypical environment” which says that the main cause for the number of particles to be large is the presence of a single very small environmental parameter Ak.

Bayesian Updates for an Extreme Value Distribution Model of Bridge Traffic Load Effect Based on SHM Data

As the distribution function of traffic load effect on bridge structures has always been unknown or very complicated, a probability model of extreme traffic load effect during service periods has not yet been perfectly predicted by the traditional extreme value theory. Here, we focus on this problem and introduce a novel method based on the bridge structural health monitoring data. The method was based on the fact that the tails of the probability distribution governed the behavior of extreme values. The generalized Pareto distribution was applied to model the tail distribution of traffic load effect using the peak-over-threshold method, while the filtered Poisson process was used to model the traffic load effect stochastic process. The parameters of the extreme value distribution of traffic load effect during a service period could be determined by theoretical derivation if the parameters of tail distribution were estimated. Moreover, Bayes’ theorem was applied to update the distribution model to reduce the statistical uncertainty. Finally, the rationality of the proposed method was applied to analyze the monitoring data of concrete-filled steel tube arch bridge suspenders. The results proved that the approach was convenient and found that the extreme value distribution type III might be more suitable as the traffic load effect probability model.

Linear dispersion relation of geodesic acoustic modes driven by trapped and circulating energetic particles

We derive the local dispersion relation of energetic-particle-induced geodesic acoustic modes (EGAMs) for both trapped and circulating ion beams with single pitch angle slowing-down and Maxwellian distributions, as well as a bump-on-tail distribution in tokamak plasmas. For slowing-down and Maxwellian particles, the solutions of the local dispersion relation give the spectrum, growth rate and thresholds of excitation as functions of the pitch angle, beam density and frequency of the energetic particles bounce motion. For circulating ions there is only one unstable branch with frequency below the GAM continuum and a threshold of excitation in the pitch angle, for both the slowing-down and single pitch Maxwellian distributions. Trapped particles cause no excitation of a mode for neither slowing-down nor Maxwellian ion beams, but they can excite a mode with a bump-on-tail distribution when the mean velocity of the beam is larger than the threshold and the energetic particle bounce frequency is high enough.

Estimation of value at risk by using gjr-garch copula based on block maxima

This paper will discuss the risk estimation of a portfolio based on value at risk (VaR) using a copula-based asymmetric Glosten – Jagannathan – Runkle - Generalized Autoregressive Conditional Heteroskedasticity (GJR-GARCH). There is non-linear correlation for dependent model structure among the variables that lead to the inaccurate VaR estimation so that we use copula functions to model the joint probability of large market movements. Data is GEV distributed. Therefore, we use Block Maxima consisting of fitting an extreme value distribution as a tail distribution to count VaR. The results show VaR can estimate the risk of portfolio return reasonably because the model has captured the data properties. Data volatility can be accommodated by GJR-GARCH, Copula can capture dependence between stocks, and Block maxima can accommodate extreme tail behavior of the data.

Pairwise deep learning to rank for top-N recommendation

Recent researches indicate that pairwise learning to rank methods could achieve high performance in dealing with data sparsity and long tail distribution in item recommendation, although suffering from problems such as high computational complexity and insufficient samples, which may cause low convergence and inaccuracy. To further improve the performance in computational capability and recommendation accuracy, in this article, a novel deep neural network based recommender architecture referred to as PDLR is proposed, in which the item corpus will be partitioned into two collections of positive instances and negative items respectively, and pairwise comparison will be performed between the positive instances and negative samples to learn the preference degree for each user. With the powerful capability of neural network, PDLR could capture rich interactions between each user and items as well as the intricate relations between items. As a result, PDLR could minimize the ranking loss, and achieve significant improvement in ranking accuracy. In practice, experimental results over four real world datasets also demonstrate the superiority of PDLR in contrast to state-of-the-art recommender approaches, in terms of Rec@N, Prec@N, AUC and NDCG@N.

On the transmission of data packets through fiber-optic cables of uniform index

The treatment of Maxwell equations show that propagating wave of packets in fiber-optic cables is dispersive, propagating in groups, such that group velocity along certain curves in the frequency-phase velocity diagrams vanishes. It is suggested that stalling of wave groups is responsible, for bursting propagation observed in experimental measurements, causing some delay in transmission. The dispersion equations developed here, are different from those given in texts that are based on “weakly guiding approximation”. The queue of such data packets arriving at a router station is found to have a “raised tail” distribution unlike that of Poisson arrivals. For accounting the property, a Mittag–Leffler function distribution (MLFD) of probability is used following a modification of that for a Poisson process, the tail raising is shown to cause delay in transmission, and its estimate is analysed based on the theory.

Imbalance and breakout in the post-epidemic era: Research into the spatial patterns of freight demand network in six provinces of central China

This study aims to explore the freight demand network spatial patterns in six provinces of central China from the perspective of the spread of the epidemic and the freight imbalance and breakout. To achieve this purpose, the big data of “cart search” demand information provided by small and medium freight enterprises on the freight information platform are analyzed. 343,690 pieces of freight demand big data on the freight information platform and Python, ArcGIS, UCINET, and Gephi software are used. The results show that: (1) The choke-point of unbalanced freight demand network is Wuhan, and the secondary choke-points are Hefei and Zhengzhou. (2) In southern China, a chain reaction circle of freight imbalance is formed with Wuhan, Hefei, and Nanchang as the centers. In northern China, a chain reaction circle of freight imbalance is formed with Zhengzhou and Taiyuan as the centers. (3) The freight demand of the six provinces in central China exhibits typical characteristics of long tail distribution with large span and unbalanced distribution. (4) The import and export of freight in different cities vary greatly, and the distribution is unbalanced. This study indicates the imbalance difference, chain reaction, keys and hidden troubles posed by the freight demand network. From the perspectives of freight transfer breakout, freight balance breakout, freight strength breakout, and breakout of freight periphery cities, we propose solutions to breakouts in the freight market in six provinces of central China in the post-epidemic era.