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.

Transient response of the 1-st order dynamic system with fluctuating parameters

1979 ◽  
Vol 44 (7) ◽  
pp. 2184-2195
Author(s):  
Vladimír Herles ◽  
Jan Čermák ◽  
Antonín Havlíček
Keyword(s):  
Dynamic System ◽  
Dynamic Behavior ◽  
Transient Response ◽  
Flow Model ◽  
Stirred Tank ◽  
Order System ◽  
Random Parameters ◽  
Stirred Tank Reactor ◽  
Tank Reactor ◽  
Theoretical Results

The paper deals with the analysis of the dynamic behavior of the 1st order system with two random parameters. The theoretical results have been compared with experiments on flow model of a stirred tank reactor.

scholarly journals Hopf Bifurcations of a Stochastic Fractional-Order Van der Pol System

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaojun Liu ◽  
Ling Hong ◽  
Lixin Yang
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Order ◽  
Stochastic System ◽  
Critical Parameter ◽  
Random Parameter ◽  
Order System ◽  
Hopf Bifurcations ◽  
Van Der Pol ◽  
Existence Conditions ◽  
Theoretical Results

The Hopf bifurcation of a fractional-order Van der Pol (VDP for short) system with a random parameter is investigated. Firstly, the Chebyshev polynomial approximation is applied to study the stochastic fractional-order system. Based on the method, the stochastic system is reduced to the equivalent deterministic one, and then the responses of the stochastic system can be obtained by numerical methods. Then, according to the existence conditions of Hopf bifurcation, the critical parameter value of the bifurcation is obtained by theoretical analysis. Then, numerical simulations are carried out to verify the theoretical results.

Adaptive Synchronization of a Stochastic Fractional-Order System

2015 ◽  
Vol 733 ◽  
pp. 939-942
Author(s):  
Xiao Jun Liu
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Stochastic System ◽  
Fractional Order System ◽  
Adaptive Synchronization ◽  
Order System ◽  
Unknown Parameters ◽  
Adaptive Laws

In this paper, adaptive synchronization of a stochastic fractional-order system with unknown parameters is studied. Firstly, the stochastic system is reduced into the equivalent deterministic one with Laguerre approximation. Then, the synchronization for the system is realized by designing appropriate controllers and adaptive laws of the unknown parameters. Numerical simulations are carried out to demonstrate the effectiveness of the controllers and laws.

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.

Analysis of a Nonlinear System with a Random Parameter

2014 ◽  
Vol 721 ◽  
pp. 366-369
Author(s):  
Hong Gang Dang ◽  
Xiao Ya Yang ◽  
Wan Sheng He
Keyword(s):  
Nonlinear System ◽  
Fractional Order ◽  
Approximation Method ◽  
Lorenz System ◽  
Laguerre Polynomial ◽  
Random Parameter ◽  
Order System ◽  
Order Complex ◽  
Ensemble Mean ◽  
Complex Lorenz System

In this paper, a nonlinear system with random parameter, which is called stochastic fractional-order complex Lorenz system, is investigated. The Laguerre polynomial approximation method is used to study the system. Then, the stochastic fractional-order system is reduced into the equivalent deterministic one with Laguerre approximation. The ensemble mean and sample responses of the stochastic system can be obtained.

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.

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).

scholarly journals Random Parameter Negative Binomial Model of Signalized Intersections

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Minho Park ◽  
Dongmin Lee ◽  
Jinwoo Jeon
Keyword(s):  
Negative Binomial ◽  
Random Parameter ◽  
Signalized Intersections ◽  
Negative Binomial Model ◽  
Marginal Effect ◽  
Binomial Model ◽  
Random Parameters ◽  
Factors Affecting ◽  
Independent Variables ◽  
Insight Into

Factors affecting accident frequencies at 72 signalized intersections in the Gyeonggi-Do (province) over a four-year period (2007~2010) were explored using the random parameters negative binomial model. The empirical results from the comparison with fixed parameters binomial model show that the random parameters model outperforms its fixed parameters counterpart and provides a fuller understanding of the factors which determine accident frequencies at signalized intersections. In addition, elasticity and marginal effect were estimated to gain more insight into the effects of one-percent and one-unit changes in the dependent variable from changes in the independent variables.

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