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Extensive high-speed railway (HSR) network resembled the intricate vascular system of the human body, crisscrossing mainlands. Seismic events, known for their unpredictability, pose a significant threat to both trains and bridges, given the HSR's extended operational duration. Therefore, ensuring the running safety of train-bridge coupled (TBC) system, primarily composed of simply supported beam bridges, is paramount. Traditional methods like the Monte Carlo method fall short in analyzing this intricate system efficiently. Instead, efficient algorithm like the new point estimate method combined with moment expansion approximation (NPEM-MEA) is applied to study random responses of numerical simulation TBC systems. Validation of the NPEM-MEA's feasibility is conducted using the Monte Carlo method. Comparative analysis confirms the accuracy and efficiency of the method, with a recommended truncation order of four to six for the NPEM-MEA. Additionally, the influences of seismic magnitude and epicentral distance are discussed based on the random dynamic responses in the TBC system. This methodology not only facilitates seismic safety assessments for TBC systems but also contributes to standard-setting for these systems under earthquake conditions. [ABSTRACT FROM AUTHOR]

Distributions of data taken from crystal structure databases, display unusual statistical properties like non-Gaussian shape, polymodality, and heavy tails. These features, typical for statistics of numerical data in social systems, appear in bigger sets (from hundreds to many thousand points) of database-originated parameters. The non-classic statistics of physical data collected through many years reflects a strong impact of social factors (financial support, exchange of information, competition, etc.) on a research activity. The values of some definite structural parameter, determined (and deposited to a database) by different authors, generally are neither independent nor random; their handling by common statistical tools may result in incorrect conclusions and wrong predictions. These statements are illustrated by several sets of reliable structural data whose statistics looks 'bad,' or inconclusive, in contemporary structural chemistry. [ABSTRACT FROM AUTHOR]

The Ensemble Kalman Filter (EnKF) is a Monte Carlo-based technique for assisted history matching and real-time updating of reservoir models. However, it often fails to detect precise locations of distinct facies boundaries and their proportions, as the facies distributions are non-Gaussian, while geologic data for reservoir modeling is usually insufficient. In this paper, a new re-sampling step is introduced to the conventional EnKF formulation; after certain number of assimilation steps, the updated ensemble is used to generate a new ensemble with a novel probability weighted re-sampling scheme. The new ensemble samples from a probability density function that is conditional to both the geological information and the early production data. After the re-sampling step, the forecast model is applied to the new ensemble from the beginning up to the last update step (without any intermediate Kalman updates). Full EnKF is again applied on the ensemble members to assimilate the remaining production history. Combination of EnKF and regenerating new members using the re-sampling method demonstrates reasonable improvement and reduction of uncertainty in history matching of reservoir models with multiple facies. The histogram and the experimental variogram of the updated ensemble members are more consistent with the static geologic information. Moreover, the technique helps maintaining ensemble variance which is essential for uncertainty estimation in the posterior probability distribution of facies proportions. [ABSTRACT FROM AUTHOR]

The general limit distributions of the sum of random variables described by a finite matrix product ansatz are characterized. Using a mapping to a Hidden Markov Chain formalism, non-standard limit distributions are obtained, and related to a form of ergodicity breaking in the underlying non-homogeneous Hidden Markov Chain. The link between ergodicity and limit distributions is detailed and used to provide a full algorithmic characterization of the general limit distributions. [ABSTRACT FROM AUTHOR]

As GARCH models and stable Paretian distributions have been revisited in the recent past with the papers of Hansen and Lunde (J Appl Econom 20: 873-889, 2005) and Bidarkota and McCulloch (Quant Finance 4: 256--265, 2004), respectively, in this paper we discuss alternative conditional distributional models for the daily returns of the US, German and Portuguese main stock market indexes, considering ARMA-GARCH models driven by Normal, Student's t and stable Paretian distributed innovations. We find that a GARCH model with stable Paretian innovations fits returns clearly better than the more popular Normal distribution and slightly better than the Student's t distribution. However, the Student's t outperforms the Normal and stable Paretian distributions when the out-of-sample density forecasts are considered. [ABSTRACT FROM AUTHOR]

We study a scenario under which variable step random walks give anomalous statistics. We begin by analyzing the Martingale Central Limit Theorem to find a sufficient condition for the limit distribution to be non-Gaussian. We study the case when the scaling index∼ζ is∼12. For corresponding continuous time processes, it is shown that the probability density function W( x; t) satisfies the Fokker–Planck equation. Possible forms for the diffusion coefficient are given, and related to W( x, t). Finally, we show how a time-series can be used to distinguish between these variable diffusion processes and Lévy dynamics. [ABSTRACT FROM AUTHOR]