Search results for "stochastic process"
showing 10 items of 346 documents
Variety and volatility in financial markets
2000
We study the price dynamics of stocks traded in a financial market by considering the statistical properties both of a single time series and of an ensemble of stocks traded simultaneously. We use the $n$ stocks traded in the New York Stock Exchange to form a statistical ensemble of daily stock returns. For each trading day of our database, we study the ensemble return distribution. We find that a typical ensemble return distribution exists in most of the trading days with the exception of crash and rally days and of the days subsequent to these extreme events. We analyze each ensemble return distribution by extracting its first two central moments. We observe that these moments are fluctua…
Analysis of the level-crossing rate and average duration of fades of WSSUS channels
2017
Studies of the level-crossing rate (LCR) and the average duration of fades (ADF) are so far only devoted to stochastic processes being a function of one independent variable, which is usually time or in some few cases frequency. In this paper, we study the LCR (ADF) of wide-sense stationary uncorrelated scattering (WSSUS) processes in the time-frequency domain. A closed-form solution will be derived for the so-called time-frequency LCR (ADF) of the absolute value of the time-variant transfer function (TVTF) of WSSUS processes. It is shown that the LCR (ADF) is circularly symmetric in the normalized time-frequency domain. The derived time-frequency LCR contains the time LCR and frequency LCR…
Fractional Laplacians in bounded domains: Killed, reflected, censored, and taboo Lévy flights.
2018
The fractional Laplacian $(- \Delta)^{\alpha /2}$, $\alpha \in (0,2)$ has many equivalent (albeit formally different) realizations as a nonlocal generator of a family of $\alpha $-stable stochastic processes in $R^n$. On the other hand, if the process is to be restricted to a bounded domain, there are many inequivalent proposals for what a boundary-data respecting fractional Laplacian should actually be. This ambiguity holds true not only for each specific choice of the process behavior at the boundary (like e.g. absorbtion, reflection, conditioning or boundary taboos), but extends as well to its particular technical implementation (Dirchlet, Neumann, etc. problems). The inferred jump-type …
ORDERING KINETICS IN QUASI-ONE-DIMENSIONAL ISING-LIKE SYSTEMS
1993
We present results of a Monte Carlo simulation of the kinetics of ordering in the two-dimensional nearest-neighbor Ising model in anL xM geometry with two free boundaries of length M≫L. This model can be viewed as representing an adsorbant on a stepped surface with mean terrace widthL. We follow the ordering kinetics after quenches to temperatures 0.25 ⩽ T/Tc ⩽ 1 starting from a random initial configuration at a coverage ofΘ=0.5 in the corresponding lattice gas picture. The systems evolve in time according to a Glauber kinetics with nonconserved order parameter. The equilibrium structure is given by a one-dimensional sequence of ordered domains. The ordering process evolves from a short ini…
Pseudo-force method for a stochastic analysis of nonlinear systems
1996
Nonlinear systems, driven by external white noise input processes and handled by means of pseudo-force theory, are transformed through simple coordinate transformation to quasi-linear systems. By means of Itô stochastic differential calculus for parametric processes, a finite hierarchy for the moment equations of these systems can be exactly obtained. Applications of this procedure to the first-order differential equation with cubic nonlinearity and to the Duffing oscillator show the versatility of the proposed method. The accuracy of the proposed procedure improves by making use of the classical equivalent linearization technique.
Dynamics of two competing species in the presence of Lévy noise sources
2010
We consider a Lotka-Volterra system of two competing species subject to multiplicative alpha-stable Lévy noise. The interaction parameter between the species is a random process which obeys a stochastic differential equation with a generalized bistable potential in the presence both of a periodic driving term and an additive alpha-stable Lévy noise. We study the species dynamics, which is characterized by two different regimes, exclusion of one species and coexistence of both. We find quasi-periodic oscillations and stochastic resonance phenomenon in the dynamics of the competing species, analysing the role of the Lévy noise sources.
Stochastic Kinetics with Wave Nature
2003
We consider stochastic second-order partial differential equations. We indroduce a noisy non-linear wave equation and discuss its connections, in particular via the Lorentz transformation, with known stochastic models.
Stochastic Nonlinear Time Series Forecasting Using Time-Delay Reservoir Computers: Performance and Universality
2014
International audience; Reservoir computing is a recently introduced machine learning paradigm that has already shown excellent performances in the processing of empirical data. We study a particular kind of reservoir computers called time-delay reservoirs that are constructed out of the sampling of the solution of a time-delay diFFerential equation and show their good performance in the forecasting of the conditional covariances associated to multivariate discrete-time nonlinear stochastic processes of VEC-GARCH type as well as in the prediction of factual daily market realized volatilities computed with intraday quotes, using as training input daily log-return series of moderate size. We …
Multivariate and Multiscale Complexity of Long-Range Correlated Cardiovascular and Respiratory Variability Series
2020
Assessing the dynamical complexity of biological time series represents an important topic with potential applications ranging from the characterization of physiological states and pathological conditions to the calculation of diagnostic parameters. In particular, cardiovascular time series exhibit a variability produced by different physiological control mechanisms coupled with each other, which take into account several variables and operate across multiple time scales that result in the coexistence of short term dynamics and long-range correlations. The most widely employed technique to evaluate the dynamical complexity of a time series at different time scales, the so-called multiscale …
Digital generation of multivariate wind field processes
2001
Abstract A very efficient procedure for the generation of multivariate wind velocity stochastic processes by wave superposition as well as autoregressive time series is proposed in this paper. The procedure starts by decomposing the wind velocity field into a summation of fully coherent independent vector processes using the frequency dependent eigenvectors of the Power Spectral Density matrix. It is shown that the application of the method allows to show some very interesting physical properties that allow to reduce drastically the computational effort. Moreover, using a standard finite element procedure for approximating the frequency dependent eigenvectors, the generation procedure requi…