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[en] We analyze a class of continuous time random walks in Rd,d≥2, with uniformly distributed directions. The steps performed by these processes are distributed according to a generalized Dirichlet law. Given the number of changes of orientation, we provide the analytic form of the probability density function of the position (Xd(t),t>0) reached, at time t > 0, by the random motion. In particular, we analyze the case of random walks with two steps. In general, it is a hard task to obtain the explicit probability distributions for the process (Xd(t),t>0). Nevertheless, for suitable values for the basic parameters of the generalized Dirichlet probability distribution, we are able to derive the explicit conditional density functions of (Xd(t),t>0). Furthermore, in some cases, by exploiting the fractional Poisson process, the unconditional probability distributions of the random walk are obtained. This paper extends in a more general setting, the random walks with Dirichlet displacements introduced in some previous papers
[en] We have investigated how uncertainties in the estimation of the detection efficiency affect the 90% confidence intervals in the unified approach for constructing confidence intervals. The study has been conducted for experiments where the number of detected events is large and can be described by a Gaussian probability density function. We also assume the detection efficiency has a Gaussian probability density and study the range of the relative uncertainties σε between 0% and 30%. We find that the confidence intervals provide proper coverage over a wide signal range and increase smoothly and continuously from the intervals that ignore scale uncertainties with a quadratic dependence on σε.
[en] The present research focuses on the statistical evaluation of Iranian plateau aftershocks from an engineering perspective and presents probabilistic models applicable for generating random earthquake scenarios. Accordingly, a comprehensive earthquake data catalog including the period from 1964 to 2016 is prepared. Data are declustered into 37 separate mainshock-aftershock sequences by considering the completeness moment magnitude of the database. The well-known modified Omori occurrence rate formula is adopted to determine the recurrence time of the events, considering the effect of secondary aftershocks. In addition to computing the probability density functions of the parameters of the Omori formula, the joint probability distribution of the aftershock occurrence versus magnitude and occurrence time is obtained for modeling their magnitude sequences. The obtained results are applicable for producing randomly generated mainshock-aftershock scenarios.
[en] In this paper, we present the stochastic foundations of fractional dynamics driven by the fractional material derivative of distributed-order type. Before stating our main result, we present the stochastic scenario which underlies the dynamics given by the fractional material derivative. Then we introduce the Lévy walk process of distributed-order type to establish our main result, which is the scaling limit of the considered process. It appears that the probability density function of the scaling limit process fulfills, in a weak sense, the fractional diffusion equation with the material derivative of distributed-order type. (paper)
[en] We present a multifractal detrended fluctuation analysis (MFDFA) of the time series of return generated by our recently-proposed Ising financial market model with underlying small world topology. The result of the MFDFA shows that there exists obvious multifractal scaling behavior in produced time series. We compare the MFDFA results for original time series with those for shuffled series, and find that its multifractal nature is due to two factors: broadness of probability density function of the series and different correlations in small- and large-scale fluctuations. This may provide new insight to the problem of the origin of multifractality in financial time series. (paper)
[en] Continuous stress-strength interference (SSI) model regards stress and strength as continuous random variables with known probability density function. This, to some extent, results in a limitation of its application. In this paper, stress and strength are treated as discrete random variables, and a discrete SSI model is presented by using the universal generating function (UGF) method. Finally, case studies demonstrate the validity of the discrete model in a variety of circumstances, in which stress and strength can be represented by continuous random variables, discrete random variables, or two groups of experimental data
[en] The present work proposes a novel methodology for constructing coarse-grained (CG) models, which aims at minimizing the difference between CG model and the corresponding original system. The difference is defined as a functional of their equilibrium conformational probability densities, then is estimated from equilibrium averages of many independent physical quantities denoted as basis functions. An orthonormalization strategy is adopted to get the independent basis functions from sufficiently preselected interesting physical quantities of the system. Thus the current method is named as probability density matching coarse-graining (PMCG) scheme, which effectively takes into account the overall characteristics of the original systems to construct CG model, and it is a natural improvement of the usual CG scheme wherein some physical quantities are intuitively chosen without considering their correlations. We verify the general PMCG framework in constructing a one-site CG water model from TIP3P model. Both structure of liquids and pressure of the TIP3P water system are found to be well reproduced at the same time in the constructed CG model. (general)
[en] We consider a decoupled continuous time random walk model with a generic waiting time probability density function (PDF). For the force-free case we derive an integro-differential diffusion equation which is related to the Galilei invariance for the probability density. We also derive a general relation which connects the nth moment in the presence of any external force to the second moment without external force, i.e. it is valid for any waiting time PDF. This general relation includes the generalized second Einstein relation, which connects the first moment in the presence of any external force to the second moment without any external force. These expressions for the first two moments are verified by using several kinds of the waiting time PDF. Moreover, we present new anomalous diffusion behaviours for a waiting time PDF given by a product of power-law and exponential function.
[en] Costa de Beauregard's proposal concerning physical retrocausality has been shown to fail on two crucial points. However, it is argued that his proposal still merits serious attention. The argument arises from showing that his proposal reveals a paradox involving relations between conditional probabilities, statistical correlations and reciprocal causalities of the type exhibited by cooperative dynamics in physical systems. 4 refs. (Author)