scholarly journals Novel anomalous diffusion phenomena of underdamped Langevin equation with random parameters

2021 ◽  
Author(s):  
Yao Chen ◽  
Xudong Wang
Keyword(s):  
Gaussian White Noise ◽  
Random Parameter ◽  
Time Dependent ◽  
Random Parameters ◽  
Velocity Correlation ◽  
Diffusion Behavior ◽  
Specific Distribution ◽  
Velocity Correlation Function ◽  
Diffusion Phenomena ◽  
Heavy Tailed

Abstract The diffusion behavior of particles moving in complex heterogeneous environment is a very topical issue. We characterize particle's trajectory via an underdamped Langevin system driven by a Gaussian white noise with a time dependent diffusivity of velocity, together with a random relaxation timescale $\tau$ to parameterize the effect of complex medium. We mainly concern how the random parameter $\tau$ influences the diffusion behavior and ergodic property of this Langevin system. Besides, the comparison between the fixed and random initial velocity $v_0$ is conducted to show the effect of different initial ensembles. The heavy-tailed distribution of $\tau$ with finite mean is found to suppress the decay rate of the velocity correlation function and promote the diffusion behavior, playing a competition role to the time dependent diffusivity. More interestingly, a random $v_0$ with a specific distribution depending on random $\tau$ also enhances the diffusion. Both the random parameters $\tau$ and $v_0$ influence the dynamics of the Langevin system in an non-obvious way, which cannot be ignored even they has finite moments.

Simplified analysis of a stochastic system

1979 ◽  
Vol 44 (2) ◽  
pp. 328-339
Author(s):  
Vladimír Herles
Keyword(s):  
Statistical Analysis ◽  
Dynamic Behavior ◽  
Stochastic System ◽  
Additive Noise ◽  
Random Parameter ◽  
Systematic Difference ◽  
Order System ◽  
Constant Parameter ◽  
Random Parameters ◽  
Simplified Analysis

Contradictious results published by different authors about the dynamics of systems with random parameters have been examined. Statistical analysis of the simple 1st order system proves that the random parameter can cause a systematic difference in the dynamic behavior that cannot be (in general) described by the usual constant-parameter model with the additive noise at the output.

scholarly journals Analysis of Severe Injury Accident Rates on Interstate Highways Using a Random Parameter Tobit Model

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Minho Park ◽  
Dongmin Lee
Keyword(s):  
Regression Model ◽  
Unobserved Heterogeneity ◽  
Random Parameter ◽  
Tobit Model ◽  
Severe Injury ◽  
Parameter Estimates ◽  
Random Parameters ◽  
Tobit Regression ◽  
Accident Rates ◽  
Tobit Regression Model

In this study, a random parameter Tobit regression model approach was used to account for the distinct censoring problem and unobserved heterogeneity in accident data. We used accident rate data (continuous data) instead of accident frequency data (discrete count data) to address the zero cell problems from data where roadway segments do not have any recorded accidents over the observed time period. The unobserved heterogeneity problem is also considered by using random parameters, which are parameter estimates that vary across observations instead of fixed parameters, which are parameter estimates that are fixed/constant over observations. Nine years (1999–2007) of panel data related to severe injury accidents in Washington State, USA, were used to develop the random parameter Tobit model. The results showed that the Tobit regression model with random parameters is a better approach to explore factors influencing severe injury accident rates on roadway segments under consideration of unobserved heterogeneity problems.

scholarly journals Clinical Factors Associated with Time-Specific Distribution of 18F-Fluorodeoxyglucose in Large-Vessel Vasculitis

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Joel S. Rosenblum ◽  
Kaitlin A. Quinn ◽  
Casey A. Rimland ◽  
Nehal N. Mehta ◽  
Mark A. Ahlman ◽  
...  
Keyword(s):  
Fdg Pet ◽  
Blood Pool ◽  
Large Vessel Vasculitis ◽  
Time Dependent ◽  
Large Vessel ◽  
Dependent Manner ◽  
Clinical Factors ◽  
Factors Associated ◽  
Fdg Uptake ◽  
Specific Distribution

Abstract 18F-fluorodeoxyglucose (FDG) positron emission tomography (PET) can detect vascular inflammation in large-vessel vasculitis (LVV). Clinical factors that influence distribution of FDG into the arterial wall and other tissues have not been characterized in LVV. Understanding these factors will inform analytic strategies to quantify vascular PET activity. Patients with LVV (n = 69) underwent 141 paired FDG-PET imaging studies at one and two hours per a delayed image acquisition protocol. Arterial uptake was quantified as standardized uptake values (SUVMax). SUVMean values were obtained for background tissues (blood pool, liver, spleen). Target-to-background ratios (TBRs) were calculated for each background tissue. Mixed model multivariable linear regression was used to identify time-dependent associations between FDG uptake and selected clinical features. Clinical factors associated with FDG distribution differed in a tissue- and time-dependent manner. Age, body mass index, and C-reactive protein were significantly associated with arterial FDG uptake at both time points. Clearance factors (e.g. glomerular filtration rate) were significantly associated with FDG uptake in background tissues at one hour but were weakly or not associated at two hours. TBRs using liver or blood pool at two hours were most strongly associated with vasculitis-related factors. These findings inform standardization of FDG-PET protocols and analytic approaches in LVV.

scholarly journals A Random Parameter Model for Continuous-Time Mean-Variance Asset-Liability Management

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Hui-qiang Ma ◽  
Meng Wu ◽  
Nan-jing Huang
Keyword(s):  
Continuous Time ◽  
Efficient Frontier ◽  
Random Parameter ◽  
Management Problem ◽  
Random Parameters ◽  
Asset Liability Management ◽  
Linear Quadratic ◽  
Liability Management ◽  
The Mean ◽  
Mean Variance

We consider a continuous-time mean-variance asset-liability management problem in a market with random market parameters; that is, interest rate, appreciation rates, and volatility rates are considered to be stochastic processes. By using the theories of stochastic linear-quadratic (LQ) optimal control and backward stochastic differential equations (BSDEs), we tackle this problem and derive optimal investment strategies as well as the mean-variance efficient frontier analytically in terms of the solution of BSDEs. We find that the efficient frontier is still a parabola in a market with random parameters. Comparing with the existing results, we also find that the liability does not affect the feasibility of the mean-variance portfolio selection problem. However, in an incomplete market with random parameters, the liability can not be fully hedged.

Time-Dependent Reliability Analysis of Vibratory Systems With Random Parameters

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Zissimos P. Mourelatos ◽  
Monica Majcher ◽  
Vasileios Geroulas
Keyword(s):  
Large Scale ◽  
Probability Of Failure ◽  
Time Dependent ◽  
Total Probability ◽  
Conditional Probabilities ◽  
Random Parameters ◽  
Random Vibrations ◽  
Input Parameters ◽  
Total Probability Theorem ◽  
Dependent Probability

The field of random vibrations of large-scale systems with millions of degrees-of-freedom (DOF) is of significant importance in many engineering disciplines. In this paper, we propose a method to calculate the time-dependent reliability of linear vibratory systems with random parameters excited by nonstationary Gaussian processes. The approach combines principles of random vibrations, the total probability theorem, and recent advances in time-dependent reliability using an integral equation involving the upcrossing and joint upcrossing rates. A space-filling design, such as optimal symmetric Latin hypercube (OSLH) sampling, is first used to sample the input parameter space. For each design point, the corresponding conditional time-dependent probability of failure is calculated efficiently using random vibrations principles to obtain the statistics of the output process and an efficient numerical estimation of the upcrossing and joint upcrossing rates. A time-dependent metamodel is then created between the input parameters and the output conditional probabilities allowing us to estimate the conditional probabilities for any set of input parameters. The total probability theorem is finally applied to calculate the time-dependent probability of failure. The proposed method is demonstrated using a vibratory beam example.

The effective long-time diffusivity for a passive scalar in a Gaussian model fluid flow

1978 ◽  
Vol 89 (2) ◽  
pp. 241-250 ◽  
Author(s):  
R. Phythian ◽  
W. D. Curtis
Keyword(s):  
Diffusion Processes ◽  
Fluid Velocity ◽  
Gaussian Model ◽  
Effective Diffusivity ◽  
Passive Scalar ◽  
Random Motion ◽  
Velocity Correlation ◽  
Molecular Diffusivity ◽  
Velocity Correlation Function ◽  
Long Time

The problem considered is the diffusion of a passive scalar in a ‘fluid’ in random motion when the fluid velocity field is Gaussian and statistically homogeneous, isotropic and stationary. A self-consistent expansion for the effective long-time diffusivity is obtained and the approximations derived from this series by retaining up to three terms are explicitly calculated for simple idealized forms of the velocity correlation function for which numerical simulations are available for comparison for zero molecular diffusivity. The dependence of the effective diffusivity on the molecular diffusivity is determined within this idealization. The results support Saffman's contention that the molecular and turbulent diffusion processes interfere destructively, in the sense that the total effective diffusivity about a fixed point is less than that which would be obtained if the two diffusion processes acted independently.

scholarly journals Synthesis of random parameter identification algorithms and estimates of current vessel motion parameters

2020 ◽  
Vol 164 ◽  
pp. 03004
Author(s):  
Nikolay Ivanovskiy ◽  
Ivan Gorychev ◽  
Aleksandr Yashin ◽  
Sergey Bidenko
Keyword(s):  
Angular Velocity ◽  
Parameter Identification ◽  
Real Time ◽  
Angular Position ◽  
Random Parameter ◽  
Moment Of Inertia ◽  
Position Vector ◽  
Random Parameters ◽  
Motion Parameters ◽  
Vessel Motion

The paper considers the task of synthesis of algorithms for identifying random parameters of a vessel, such as attached masses, moment of inertia, and estimating the current parameters of the vessel's motion from real-time measurements of onboard sensors. The task of the synthesis of algorithms for identifying random parameters of the vessel and evaluating the characteristics of the vessel’s movement is to determine (evaluate) the current parameters (attached masses, moment of inertia) and the characteristics of the vessel’s motion (position vector, speed) from the measurements of the vessel’s motion, angular position and angular velocity of the vessel rotation).

Sign in / Sign up

Export Citation Format

Share Document