Search results for "Stochastic process"
showing 10 items of 346 documents
Lévy walks and scaling in quenched disordered media.
2010
We study L\'evy walks in quenched disordered one-dimensional media, with scatterers spaced according to a long-tailed distribution. By analyzing the scaling relations for the random-walk probability and for the resistivity in the equivalent electric problem, we obtain the asymptotic behavior of the mean square displacement as a function of the exponent characterizing the scatterers distribution. We demonstrate that in quenched media different average procedures can display different asymptotic behavior. In particular, we estimate the moments of the displacement averaged over processes starting from scattering sites, in analogy with recent experiments. Our results are compared with numerical…
Markov Chain and Stationary Distribution
2019
MC has been a valuable tool for analyzing the performance of complex stochastic systems since it was introduced by the Russian mathematician A. A. Markov (1856–1922) in the early 1900s. More and more system analyses have been carried out by using MC, including the analysis on CA and CF. In this chapter, we will briefly review the essential ingredients of MC that are necessary for the performance analysis presented in this book. A more comprehensive introduction of MC and its applications can be found in Nelson (2013, Probability, stochastic processes, and queueing theory: the mathematics of computer performance modeling).
Including Covariates in the ETAS Model Triggered Seismicity
2020
The paper proposes a stochastic process that improves the assessment of seismic events in space and time, considering a contagion model (branching process) within a regression-like framework to take covariates into account. The proposed approach develops the Forward Likelihood for prediction (FLP) method for estimating the ETAS model, including covariates in the model specification of the epidemic component. A simulation study is carried out for analysing the misspecification model effect under several scenarios. Also an application to the Italian catalogue is reported, together with the reference to the developed R package.
Analysis of random walks on a hexagonal lattice
2019
We consider a discrete-time random walk on the nodes of an unbounded hexagonal lattice. We determine the probability generating functions, the transition probabilities and the relevant moments. The convergence of the stochastic process to a 2-dimensional Brownian motion is also discussed. Furthermore, we obtain some results on its asymptotic behavior making use of large deviation theory. Finally, we investigate the first-passage-time problem of the random walk through a vertical straight-line. Under suitable symmetry assumptions we are able to determine the first-passage-time probabilities in a closed form, which deserve interest in applied fields.
Tool-life modelling as a stochastic process
1998
Abstract In a previous paper [G. Galante, A. Lombardo, A. Passannanti, Proceedings of XXXVII Scientific Meeting of the Italian Statistical Society, 1994, p. 553] the Authors proposed to model cutting tool wear behaviour as a stochastic process with independent Gaussian increments plus drift. Such a model implies that the tool-life, i.e. the time to reach a fixed value of flank wear, has an inverse Gaussian probability distribution. The model has several practical and theoretical advantages. In fact, it is based on an easily and cheaply experimentally verifiable wear behaviour hypothesis, it is more flexible because it is not limited to a particular wear level and, finally, the data are bett…
A non-stationary one-ring scattering model
2013
This paper introduces a non-stationary one-ring scattering model in which the mobile station (MS) can move along a straight line from the ring's center to the border of the ring. This movement results in a time-variant angle-of-arrival (AOA), which is modeled by a stochastic process. We derive the first-order density of the AOA process in closed form. Subsequently, a closed-form expression is provided for the local power spectral density (PSD) of the channel. We also formulate the local autocorrelation function (ACF) of the complex channel gain in integral form, from which a highly accurate closed-form approximation is derived. Furthermore, the average Doppler shift and the Doppler spread o…
Risk Assessment of Toxicants to Pelagic Food-Webs: A Simulation Study
1991
For a generalized mathematical model of the pelagic compartment of a lake ecosystem we show that a small variance in input parameters may result in a large variance in predicted biomasses. Since input parameters for this kind of models always show a great variance, we conclude that deterministic prediction of biomass-trajectories is rather useless and demonstrate how stochastic analysis of the model may lead to a helpful risk analysis.
Pleistocene allopatric differentiation followed by recent range expansion explains the distribution and molecular diversity of two congeneric crustac…
2021
AbstractPleistocene glaciations had a tremendous impact on the biota across the Palaearctic, resulting in strong phylogeographic signals of range contraction and rapid postglacial recolonization of the deglaciated areas. Here, we explore the diversity patterns and history of two sibling species of passively dispersing taxa typical of temporary ponds, fairy shrimps (Anostraca). We combine mitochondrial (COI) and nuclear (ITS2 and 18S) markers to conduct a range-wide phylogeographic study including 56 populations of Branchinecta ferox and Branchinecta orientalis in the Palaearctic. Specifically, we investigate whether their largely overlapping ranges in Europe resulted from allopatric differe…
A modal approach for the evaluation of the response sensitivity of structural systems subjected to non-stationary random processes
2005
A method for the evaluation of the response sensitivity of both classically and non-classically damped discrete linear structural systems under stochastic actions is presented. The proposed approach requires the following items: (a) a suitable modal expansion of the response; (b) the derivation in analytical form of the equations governing the evolution of the derivatives of the response (the so-called sensitivity equations) with respect to the parameters that define the structural model; (c) an extensive use of the Kronecker algebra for determining the analytical expressions of the sensitivity of the structural response statistics to non-stationary random input processes. Moreover, a step-…
A neural network approach to movement pattern analysis.
2004
Movements are time-dependent processes and so can be modelled by time-series of coordinates: E.g., each articulation has geometric coordinates; the set of the coordinates of the relevant articulations build a high-dimensional configuration. These configurations--or "patterns"--give reason for analysing movements by means of neural networks: The Kohonen Feature Map (KFM) is a special type of neural network, which (after having been coined by training with appropriate pattern samples) is able to recognize single patterns as members of pattern clusters. This way, for example, the particular configurations of a given movement can be identified as belonging to respective configuration clusters, …