Symmetric Skorohod topology onn-variable functions and hierarchical Markov properties ofn-parameter processes

1995 ◽  
Vol 103 (1) ◽  
pp. 25-43 ◽  
Author(s):  
F. Hirsch ◽  
S. Song
Keyword(s):  
Skorohod Topology ◽  
Markov Properties

scholarly journals Markov properties of cluster processes

1996 ◽  
Vol 28 (2) ◽  
pp. 346-355 ◽  
Author(s):  
A. J. Baddeley ◽  
M. N. M. Van Lieshout ◽  
J. Møller
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Markov Property ◽  
Nearest Neighbour ◽  
Finite Range ◽  
Cluster Process ◽  
Cluster Point Process ◽  
Poisson Cluster ◽  
Markov Properties ◽  
Uniformly Bounded

We show that a Poisson cluster point process is a nearest-neighbour Markov point process [2] if the clusters have uniformly bounded diameter. It is typically not a finite-range Markov point process in the sense of Ripley and Kelly [12]. Furthermore, when the parent Poisson process is replaced by a Markov or nearest-neighbour Markov point process, the resulting cluster process is also nearest-neighbour Markov, provided all clusters are non-empty. In particular, the nearest-neighbour Markov property is preserved when points of the process are independently randomly translated, but not when they are randomly thinned.

scholarly journals A Note on Equivalence Classes of Directed Acyclic Independence Graphs

1993 ◽  
Vol 7 (3) ◽  
pp. 409-412 ◽  
Author(s):  
David Madigan
Keyword(s):  
Model Selection ◽  
Expert Systems ◽  
Equivalence Classes ◽  
Influence Diagrams ◽  
Single Class ◽  
Selection Procedures ◽  
Probabilistic Expert Systems ◽  
Recent Developments ◽  
Independence Graphs ◽  
Markov Properties

Directed acyclic independence graphs (DAIGs) play an important role in recent developments in probabilistic expert systems and influence diagrams (Chyu [1]). The purpose of this note is to show that DAIGs can usefully be grouped into equivalence classes where the members of a single class share identical Markov properties. These equivalence classes can be identified via a simple graphical criterion. This result is particularly relevant to model selection procedures for DAIGs (see, e.g., Cooper and Herskovits [2] and Madigan and Raftery [4]) because it reduces the problem of searching among possible orientations of a given graph to that of searching among the equivalence classes.

Markov properties of multiparameter processes and capacities

1995 ◽  
Vol 103 (1) ◽  
pp. 45-71 ◽  
Author(s):  
F. Hirsch ◽  
S. Song
Keyword(s):  
Markov Properties

Markov Properties for Mixed Graphical Models

2018 ◽  
pp. 39-60
Author(s):  
Robin Evans
Keyword(s):  
Graphical Models ◽  
Markov Properties

scholarly journals Markov properties for mixed graphs

Bernoulli ◽  
2014 ◽  
Vol 20 (2) ◽  
pp. 676-696 ◽  
Author(s):  
Kayvan Sadeghi ◽  
Steffen Lauritzen
Keyword(s):  
Mixed Graphs ◽  
Markov Properties

Sets with the Bernstein and generalized Markov properties

2014 ◽  
Vol 111 (3) ◽  
pp. 259-270 ◽  
Author(s):  
Mirosław Baran ◽  
Agnieszka Kowalska
Keyword(s):  
Markov Properties

scholarly journals Scaling property of ideal granitic sequences

2007 ◽  
Vol 14 (3) ◽  
pp. 237-246 ◽  
Author(s):  
D. Xu ◽  
Q. Cheng ◽  
F. Agterberg
Keyword(s):  
Lake Area ◽  
Fine Grained ◽  
Multi Scale ◽  
Invariance Properties ◽  
The Past ◽  
Ideal Granite ◽  
Markov Properties ◽  
The Ideal

Abstract. Quantification of granite textures and structures using a mathematical model for characterization of granites has been a long-term attempt of mathematical geologists over the past four decades. It is usually difficult to determine the influence of magma properties on mineral crystallization forming fined-grained granites due to its irregular and fine-grained textures. The ideal granite model was originally developed for modeling mineral sequences from first and second-order Markov properties. This paper proposes a new model for quantifying scale invariance properties of mineral clusters and voids observed within mineral sequences. Sequences of the minerals plagioclase, quartz and orthoclase observed under the microscope for 104 aplite samples collected from the Meech Lake area, Gatineau Park, Québec were used for validation of the model. The results show that the multi-scale approaches proposed in this paper may enable quantification of the nature of the randomness of mineral grain distributions. This, in turn, may be related to original properties of the magma.

scholarly journals Markov properties of solar granulation

2008 ◽  
Vol 494 (1) ◽  
pp. 287-294 ◽  
Author(s):  
A. Asensio Ramos
Keyword(s):  
Solar Granulation ◽  
Markov Properties
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