Necessary conditions for Markovian processes on a lattice

1973 ◽  
Vol 10 (3) ◽  
pp. 605-612 ◽  
Author(s):  
P. A. P. Moran
Keyword(s):  
Gaussian Processes ◽  
Spectral Distribution ◽  
Necessary Conditions ◽  
Square Lattice ◽  
Stationary Processes ◽  
Nearest Neighbour ◽  
Markovian Processes ◽  
Linearity Of Regression ◽  
The Difference ◽  
Non Gaussian

Stationary processes which are defined on the points of a square lattice and are Markovian in various senses are considered. It is shown that a certain assumption of linearity of regression forces the spectral distribution to be of a certain explicit form, and that given this form Gaussian processes of this kind are easily constructed. Certain non-Gaussian processes satisfying the various Markovian properties are also constructed and the difference from nearest-neighbour systems emphasized. It is conjectured, but not proved, that the assumption of linearity of regression also implies Gaussianity.

Necessary conditions for Markovian processes on a lattice

1973 ◽  
Vol 10 (03) ◽  
pp. 605-612 ◽  
Author(s):  
P. A. P. Moran
Keyword(s):  
Gaussian Processes ◽  
Spectral Distribution ◽  
Necessary Conditions ◽  
Square Lattice ◽  
Stationary Processes ◽  
Nearest Neighbour ◽  
Markovian Processes ◽  
Linearity Of Regression ◽  
The Difference ◽  
Non Gaussian

Stationary processes which are defined on the points of a square lattice and are Markovian in various senses are considered. It is shown that a certain assumption of linearity of regression forces the spectral distribution to be of a certain explicit form, and that given this form Gaussian processes of this kind are easily constructed. Certain non-Gaussian processes satisfying the various Markovian properties are also constructed and the difference from nearest-neighbour systems emphasized. It is conjectured, but not proved, that the assumption of linearity of regression also implies Gaussianity.

scholarly journals Structure factors for generalized grey Browinian motion

2019 ◽  
Vol 22 (2) ◽  
pp. 396-411
Author(s):  
José L. da Silva ◽  
Ludwig Streit
Keyword(s):  
Gaussian Processes ◽  
Form Factors ◽  
Analytic Form ◽  
Debye Function ◽  
Asymptotic Decay ◽  
Structure Factors ◽  
Closed Analytic Form ◽  
Non Gaussian

Abstract In this paper we investigate the form factors of paths for a class of non Gaussian processes. These processes are characterized in terms of the Mittag-Leffler function. In particular, we obtain a closed analytic form for the form factors, the Debye function, and can study their asymptotic decay.

scholarly journals Effect of grouping on behaviour of dairy heifers and cows in the transition period

2021 ◽  
pp. 1-7
Author(s):  
Maria Soonberg ◽  
Marko Kass ◽  
Tanel Kaart ◽  
Rosie Barraclough ◽  
Marie J. Haskell ◽  
...  
Keyword(s):  
Transition Period ◽  
Dairy Farm ◽  
Video Camera ◽  
Nearest Neighbour ◽  
Housing Systems ◽  
Dairy Heifers ◽  
Lactation Stage ◽  
Cubicle Housing ◽  
The Difference ◽  
The Right

Abstract Regrouping dairy cows is a common feature of dairy farm management. Cows are grouped based on lactation stage, age, milk yield and other factors. Regrouping cows during the dry period (from far-off area to close up area and from close up area to the main herd) brings new challenges. This is especially true for heifers who, after being confirmed gravid, may be grouped into a new pen with dried off cows. The aims of this study were to determine how grouping affects activity, nearest neighbour relationships and aggression, and how heifers’ acclimatization to a new group differs from cows. Therefore, the hypotheses were that regrouping cows has less of an effect on older cows compared to heifers, and cows' individuality affects acclimatization to a new group. Aggression data were recorded using a video camera that was directed at the feed bunk, and activity was recorded with activity monitors that were attached around the right hind leg. Synchrony and distance to nearest neighbour were recorded, as was the cows' location on the first 3 d from the day they returned to the main herd. Motion index, mean number of steps and number of lying bouts were significantly higher after calving compared to the week before calving and the difference was higher amongst heifers compared to cows (P < 0.001). Both cows and heifers lay down more in the strawyard compared to cubicle housing (P < 0.01) and cows were more aggressive than heifers in both housing systems (P < 0.001 and P < 0.05, respectively). As hypothesized, heifers were more affected by regrouping and cows with more experience settled quicker to their new environment.

scholarly journals Gaussian and non-Gaussian processes of zero power variation

2015 ◽  
Vol 19 ◽  
pp. 414-439 ◽  
Author(s):  
Francesco Russo ◽  
Frederi Viens
Keyword(s):  
Gaussian Processes ◽  
Power Variation ◽  
Non Gaussian

Decomposing the Non-Gaussian Surface in Sum of Gaussian Surfaces

2012 ◽  
Vol 580 ◽  
pp. 170-174
Author(s):  
Zhang Xing Qi ◽  
Zhen Sen Wu ◽  
Zi Wen Yu ◽  
Hai Ying Li
Keyword(s):  
Cross Section ◽  
Electromagnetic Scattering ◽  
Radar Cross Section ◽  
Kirchhoff Approximation ◽  
Munk Function ◽  
The Difference ◽  
Non Gaussian ◽  
Gaussian Surface

The decomposition of the multivariate Non-Gaussian PDF in the sum of a Gaussian PDF instead of the Gram-Charlier series is investigated. Four parameters need to be found by minimizing the integrated square of the difference between Cox-Munk function and its approximation. The backscattering radar cross section (RCS) of the surface is calculated by the Kirchhoff approximation (KA) under different value of k using the formula of decomposition of the Non-Gaussian. The condition of KA satisfying electromagnetic scattering scale from Gaussian and Non-Gaussian surfaces is taken into account by computing the backscattering coefficients in HH and VV polarity.

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