A first-order autoregressive model for the joint distribution of a time dependent random variable and its derivative

2011 ◽  
Vol 22 (7) ◽  
pp. 826-846
Author(s):  
Nils Mole ◽  
Lawrence Chan
Keyword(s):  
Autoregressive Model ◽  
Joint Distribution ◽  
Dependent Random Variable ◽  
Random Variable ◽  
Time Dependent ◽  
First Order

PATH INTEGRAL METHOD FOR LIMITING DISTRIBUTION OF AN ESTIMATOR ARISING FROM AN AR(1)-PROCESS WITH A UNIT ROOT

2013 ◽  
Vol 16 (04) ◽  
pp. 1350029
Author(s):  
SHIH-FENG HUANG ◽  
YUH-JIA LEE ◽  
HSIN-HUNG SHIH
Keyword(s):  
Characteristic Function ◽  
Path Integral ◽  
Unit Root ◽  
Autoregressive Model ◽  
Integral Method ◽  
Unit Root Test ◽  
Random Variable ◽  
Limiting Distribution ◽  
First Order ◽  
Path Integral Method

We propose the path-integral technique to derive the characteristic function of the limiting distribution of the unit root test in a first order autoregressive model. Our results provide a new and useful approach to obtain the closed form of the characteristic function of a random variable associated with the limiting distribution, which is realized as a ratio of Brownian functionals on the classical Wiener space.

MODELLING NITROGEN PROCESSES IN SOIL: MATHEMATICAL DEVELOPMENT AND RELATIONSHIPS

1976 ◽  
Vol 56 (2) ◽  
pp. 71-78 ◽  
Author(s):  
D. R. CAMERON ◽  
C. G. KOWALENKO
Keyword(s):  
Time Dependent ◽  
Rate Coefficients ◽  
Nitrification Rate ◽  
Order Kinetic ◽  
Nitrogen Flow ◽  
First Order ◽  
Interaction Term ◽  
Flow Pathways ◽  
Adsorption Desorption ◽  
Temperature Water

A small subsystem model was developed to simulate the major nitrogen flow pathways in an unsaturated soil treated with ammonium sulphate. A nonlinear Freundlich equilibrium model and a Langmuir kinetic model were used to describe mathematically the adsorption–desorption of soluble NH4+ to the exchangeable and clay-fixed phases, respectively. Time dependent, microbial mediated first-order kinetic models were used to quantify the ammonification and nitrification processes. The subsystem model was then used as a research tool to derive ammonification and nitrification rate coefficients for a preceding incubation experiment conducted using different soil moisture contents and temperatures. The model yields reasonably good fits to the observed data. A subsequent regression analysis relating the coefficients to temperature and moisture pointed out the importance of the temperature–water content interaction term in quantifying microbial mediated processes.

The flow properties of honey–malt spread

2017 ◽  
Vol 23 (5) ◽  
pp. 415-425 ◽  
Author(s):  
M Dianat ◽  
M Taghizadeh ◽  
F Shahidi ◽  
SMA Razavi
Keyword(s):  
Flow Behavior ◽  
Time Dependent ◽  
Malt Extract ◽  
Barley Malt ◽  
First Order ◽  
Dependent Behavior ◽  
Thixotropic Behaviour ◽  
Order Stress ◽  
Temperature Levels ◽  
Independent Behavior

In this study, the effect of barley malt extract at two brix levels (74 and 79 °Bx) and three ratios of malt extract/honey (65:35, 70:30 and 75:25) on the flow behavior properties of honey–malt spread at three temperature levels (35 ℃, 45 ℃ and 55 ℃) was investigated. Time-dependent behavior data of the spread samples were appropriately fitted to the Weltman, first-order stress decay with a zero stress value and first-order stress decay with a non-zero stress value models. Also, the Power-law, Herschel–Bulkley, Casson and Bingham models were used for curve fitting the time-independent behavior data. Regarding the R2 and root mean square error coefficients, the first-order stress decay with a non-zero stress value and Herschel–Bulkley models were selected as the suitable models to describe the flow behavior of samples. The results for time-dependent properties showed that spread samples exhibit a thixotropic behaviour, as the viscosity for all samples decreased with increase in shearing time at a constant shear rate of 50 s−1.

Upstream motions in stratified flow

1988 ◽  
Vol 187 ◽  
pp. 487-506 ◽  
Author(s):  
I. P. Castro ◽  
W. H. Snyder
Keyword(s):  
Body Height ◽  
Three Dimensional ◽  
Time Dependent ◽  
Experimental Measurements ◽  
Two Dimensional ◽  
Towing Tank ◽  
First Order ◽  
Density Perturbations ◽  
Small Obstacle ◽  
Obstacle Height

In this paper experimental measurements of the time-dependent velocity and density perturbations upstream of obstacles towed through linearly stratified fluid are presented. Attention is concentrated on two-dimensional obstacles which generate turbulent separated wakes at Froude numbers, based on velocity and body height, of less than 0.5. The form of the upstream columnar modes is shown to be largely that of first-order unattenuating disturbances, which have little resemblance to the perturbations described by small-obstacle-height theories. For two-dimensional obstacles the disturbances are similar to those found by Wei, Kao & Pao (1975) and it is shown that provided a suitable obstacle drag coefficient is specified, the lowest-order modes (at least) are quantitatively consistent with the results of the Oseen inviscid model.Discussion of some results of similar measurements upstream of three-dimensional obstacles, the importance of towing tank endwalls and the relevance of the Foster & Saffman (1970) theory for the limit of zero Froude number is also included.

Dynamic Stability of an Axially Moving Yarn with Time-Dependent Tension

2014 ◽  
Vol 900 ◽  
pp. 753-756 ◽  
Author(s):  
You Guo Li
Keyword(s):  
Differential Equation ◽  
Homotopy Perturbation Method ◽  
Time Dependent ◽  
Second Law ◽  
Order Ordinary Differential Equation ◽  
Vibration Equation ◽  
Transversal Vibration ◽  
First Order ◽  
Homotopy Perturbation ◽  
Axially Moving

In this paper the nonlinear transversal vibration of axially moving yarn with time-dependent tension is investigated. Yarn material is modeled as Kelvin element. A partial differential equation governing the transversal vibration is derived from Newtons second law. Galerkin method is used to truncate the governing nonlinear differential equation, and thus first-order ordinary differential equation is obtained. The periodic vibration equation and the natural frequency of moving yarn are received by applying homotopy perturbation method. As a result, the condition which should be avoided in the weaving process for resonance is obtained.

Mixture copulas and insurance applications

2018 ◽  
Vol 12 (2) ◽  
pp. 391-411
Author(s):  
Maissa Tamraz
Keyword(s):  
Joint Distribution ◽  
Stable Distribution ◽  
Random Variable ◽  
Fixed Time ◽  
Collective Model ◽  
Data Sets ◽  
New Model ◽  
Time Period ◽  
Insurance Data ◽  
Dependence Property

AbstractIn the classical collective model over a fixed time period of two insurance portfolios, we are interested, in this contribution, in the models that relate to the joint distributionFof the largest claim amounts observed in both insurance portfolios. Specifically, we consider the tractable model where the claim counting random variableNfollows a discrete-stable distribution with parameters (α,λ). We investigate the dependence property ofFwith respect to both parametersαandλ. Furthermore, we present several applications of the new model to concrete insurance data sets and assess the fit of our new model with respect to other models already considered in some recent contributions. We can see that our model performs well with respect to most data sets.

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