Search results for "PROBABILITY DENSITY"
showing 10 items of 187 documents
Statistics of residence time for Lévy flights in unstable parabolic potentials
2020
We analyze the residence time problem for an arbitrary Markovian process describing nonlinear systems without a steady state. We obtain exact analytical results for the statistical characteristics of the residence time. For diffusion in a fully unstable potential profile in the presence of Lévy noise we get the conditional probability density of the particle position and the average residence time. The noise-enhanced stability phenomenon is observed in the system investigated. Results from numerical simulations are in very good agreement with analytical ones.
Anomalous diffusion and nonlinear relaxation phenomena in stochastic models of interdisciplinary physics
2020
The study of nonlinear dynamical systems in the presence of both Gaussian and non-Gaussian noise sources is the topic of this research work. In particular, after shortly present new theoretical results for statistical characteristics in the framework of Markovian theory, we analyse four different physical systems in the presence of Levy noise source. (a) The residence time problem of a particle subject to a non-Gaussian noise source in arbitrary potential profile was analyzed and the exact analytical results for the statistical characteristics of the residence time for anomalous diffusion in the form of Levy flights in fully unstable potential profile was obtained. Noise enhanced stability …
A Fokker–Planck control framework for multidimensional stochastic processes
2013
AbstractAn efficient framework for the optimal control of probability density functions (PDFs) of multidimensional stochastic processes is presented. This framework is based on the Fokker–Planck equation that governs the time evolution of the PDF of stochastic processes and on tracking objectives of terminal configuration of the desired PDF. The corresponding optimization problems are formulated as a sequence of open-loop optimality systems in a receding-horizon control strategy. Many theoretical results concerning the forward and the optimal control problem are provided. In particular, it is shown that under appropriate assumptions the open-loop bilinear control function is unique. The res…
Solving fully randomized first-order linear control systems: Application to study the dynamics of a damped oscillator with parametric noise under sto…
2022
[EN] This paper is devoted to study random linear control systems where the initial condition, the final target, and the elements of matrices defining the coefficients are random variables, while the control is a stochastic process. The so-called Random Variable Transformation technique is adapted to obtain closed-form expressions of the probability density functions of the solution and of the control. The theoretical findings are applied to study the dynamics of a damped oscillator subject to parametric noise.
Interdependence Between Tool Fracture and Wear
1985
Wear and fracture are the main causes of tool scrapping. However fracture plays a major role for increasing values of the hardness and brittleness of tool materials or when low-cobalt tungsten carbides are used or in interrupted cutting conditions where it is the most relevant factor for tool scrapping. In order to obtain the optimal values of the cutting speed both these factors should be considered. The hypothesis of stochastic independence among them simplifies the mathematical formulation of the optimization problem; but experimental investigations do not agree with this assumption and, as a matter of fact, the probability density function of tool fracture results to be dependent on the…
Einstein-Smoluchowsky equation handled by complex fractional moments
2014
In this paper the response of a non linear half oscillator driven by α-stable white noise in terms of probability density function (PDF) is investigated. The evolution of the PDF of such a system is ruled by the so called Einstein-Smoluchowsky equation involving, in the diffusive term, the Riesz fractional derivative. The solution is obtained by the use of complex fractional moments of the PDF, calculated with the aid of Mellin transform operator. It is shown that solution can be found for various values of stability index α and for any nonlinear function of the drift term in the stochastic differential equation.
Exact stationary solution for a class of non-linear systems driven by a non-normal delta-correlated process
1995
In this paper the exact stationary solution in terms of probability density function for a restricted class of non-linear systems under both external and parametric non-normal delta-correlated processes is presented. This class has been obtained by imposing a given probability distribution and finding the corresponding dynamical system which satisfies the modified Fokker-Planck equation. The effectiveness of the results has been verified by means of a Monte Carlo simulation.
A Scenario Simulation Model of Stock's Volatility Based on a Stationary Markovian Process
2013
In this paper we discuss univariate statistical properties of volatility. We present a parsimonious univariate model that well reproduces two stylized facts of volatility: the power-law decay of the volatility probability density function with exponent α and the power-law decay of the autocorrelation function with exponent β. Such model also reproduces, at least qualitatively, the empirical observation than when the probability density function decays faster, then the autocorrelation decays slower. Another important feature investigated within the model is the mean First Passage Time (mFPT) Tx0 (Λ) of volatility time-series. We show that the proposed model allows to obtain the mFPT in terms…
Numerical simulation of resonant activation in a fluctuating metastable model system
1998
We study the escape time from a metastable overdamped model system in the presence of two noise sources: a white noise and a random telegraph noise. The random telegraph noise controls the height of the potential barrier of the metastable system while the white noise mimics the presence of a given temperature. We report on numerical simulations about: (i) the average residence time of the system in the metastable state; (ii) the probability density function (PDF) of the residence time at various values of the correlation time T c of the random telegraph noise. Resonant activation is observed in the dynamics of the investigated system. The PDF shows different shapes for different values of τ…
SAVU: A Statistical Approach for Uncertain Data in Dynamics of Axially Moving Materials
2012
In physics and engineering problems, model input is never exact. The effect of small uncertainties on the solution is thus an important question. In this study, a direct statistical-visual approach to approximate the solution set is investigated in the context of axially moving materials. The multidimensional probability distribution for the input uncertainties is assumed known. It is considered as a deterministic object, which is then mapped through the model. The resulting probability density of the model output is visualized. The proposed system consists of three non-trivial parts, which are briefly discussed: a multidimensional sampler, a density estimator, and a high dynamic range (HDR…