scholarly journals Evaluating height structure in Scots pine forests using marked point processes

2008 ◽  
Vol 38 (7) ◽  
pp. 1924-1934 ◽  
Author(s):  
Fernando Montes ◽  
Ignacio Barbeito ◽  
Agustín Rubio ◽  
Isabel Cañellas
Keyword(s):  
Scots Pine ◽  
Point Processes ◽  
Marked Point ◽  
Null Model ◽  
Tree Height ◽  
Moment Analysis ◽  
Marked Point Processes ◽  
Height Distribution ◽  
Second Moment ◽  
Point Patterns

In this study, the second-moment analysis of marked spatial point processes is applied to the characterization of the tree height distribution in two Scots pine ( Pinus sylvestris L.) forests in the Central Mountain Range of Spain. The cumulative function Lm(d) weighted by the normalized mark variance is proposed to analyse the second-order properties of marked point patterns. The empirical Lm(d) was compared with two null models to assess the relationship between the spatial distribution of the trees and the tree height correlations: the first null model was used to characterize the spatial clustering of the trees and was derived from the complete spatial randomness model used with Ripley’s K(d) function. The second null model, which is derived from the random labelling model used with the intertype second-moment measure K12(d) (type 1 intensity conditioned to the type 2 intensity and vice versa), allows us to identify the mark correlations. The performance of the technique was assessed through simulated marked point patterns. The second-moment analysis showed that most of the analysed Scots pine stands have a uniform height distribution at small scale and greater heterogeneity at large scales, with the exception of an upper altitudinal stand, which exhibited heterogeneity at short distances. These results demonstrate the utility of second-moment analysis of marked point processes for characterizing height structure in forest stands and the interaction between the height and the spatial pattern of the trees.

Marked point processes as limits of Markovian arrival streams

1993 ◽  
Vol 30 (02) ◽  
pp. 365-372 ◽  
Author(s):  
Søren Asmussen ◽  
Ger Koole
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Marked Point ◽  
The State ◽  
Marked Point Processes ◽  
Marked Point Process ◽  
State Transitions ◽  
Poisson Arrival ◽  
Convergence Of Moments ◽  
Environmental Process

A Markovian arrival stream is a marked point process generated by the state transitions of a given Markovian environmental process and Poisson arrival rates depending on the environment. It is shown that to a given marked point process there is a sequence of such Markovian arrival streams with the property that as m →∞. Various related corollaries (involving stationarity, convergence of moments and ergodicity) and counterexamples are discussed as well.

scholarly journals Perfect sampling for infinite server and loss systems

2015 ◽  
Vol 47 (03) ◽  
pp. 761-786 ◽  
Author(s):  
Jose Blanchet ◽  
Jing Dong
Keyword(s):  
Point Processes ◽  
Marked Point ◽  
Heavy Traffic ◽  
Arrival Rate ◽  
Marked Point Processes ◽  
Perfect Sampling ◽  
Running Time ◽  
Infinite Server ◽  
Loss Systems ◽  
Server System

We present the first class of perfect sampling (also known as exact simulation) algorithms for the steady-state distribution of non-Markovian loss systems. We use a variation of dominated coupling from the past. We first simulate a stationary infinite server system backwards in time and analyze the running time in heavy traffic. In particular, we are able to simulate stationary renewal marked point processes in unbounded regions. We then use the infinite server system as an upper bound process to simulate the loss system. The running time analysis of our perfect sampling algorithm for loss systems is performed in the quality-driven (QD) and the quality-and-efficiency-driven regimes. In both cases, we show that our algorithm achieves subexponential complexity as both the number of servers and the arrival rate increase. Moreover, in the QD regime, our algorithm achieves a nearly optimal rate of complexity.

scholarly journals Random Marked Sets

2012 ◽  
Vol 44 (3) ◽  
pp. 603-616 ◽  
Author(s):  
F. Ballani ◽  
Z. Kabluchko ◽  
M. Schlather
Keyword(s):  
Random Fields ◽  
Covariance Function ◽  
Point Processes ◽  
Marked Point ◽  
Positive Definiteness ◽  
Gaussian Random Fields ◽  
Marked Point Processes ◽  
Random Set ◽  
Geostatistical Methods ◽  
New Class

We aim to link random fields and marked point processes, and, therefore, introduce a new class of stochastic processes which are defined on a random set in . Unlike for random fields, the mark covariance function of a random marked set is in general not positive definite. This implies that in many situations the use of simple geostatistical methods appears to be questionable. Surprisingly, for a special class of processes based on Gaussian random fields, we do have positive definiteness for the corresponding mark covariance function and mark correlation function.

Some EATA properties for marked point processes

1995 ◽  
Vol 32 (04) ◽  
pp. 922-929
Author(s):  
D. Kofman ◽  
H. Korezlioglu
Keyword(s):  
Point Processes ◽  
Stochastic Integral ◽  
Marked Point ◽  
Marked Point Processes ◽  
Batch Arrival ◽  
Integral Approach ◽  
Arrival Processes

We derive an ESTA property for marked point processes similar to Wolff's PASTA property for ordinary (non-marked) point processes, via a stochastic integral approach. This new ESTA property allows us to extend a known result on the conditional PASTA property and to derive an ASTA property for batch arrival processes. We also present an application of our results.

Integral equations for compound distribution functions

1996 ◽  
Vol 33 (2) ◽  
pp. 388-399 ◽  
Author(s):  
Christian Max Møller
Keyword(s):  
Point Processes ◽  
Marked Point ◽  
Building Blocks ◽  
Distribution Functions ◽  
Jump Processes ◽  
Marked Point Processes ◽  
Martingale Theory ◽  
Compound Distribution ◽  
Change Of Variable ◽  
Fixed Period

The aim of the present paper is to introduce some techniques, based on the change of variable formula for processes of finite variation, for establishing (integro) differential equations for evaluating the distribution of jump processes for a fixed period of time. This is of interest in insurance mathematics for evaluating the distribution of the total amount of claims occurred over some period of time, and attention will be given to such issues. Firstly we will study some techniques when the process has independent increments, and then a more refined martingale technique is discussed. The building blocks are delivered by the theory of marked point processes and associated martingale theory. A simple numerical example is given.

Marked Point Processes for Microarray Data Clustering

2017 ◽  
pp. 133-147 ◽  
Author(s):  
Khadidja Henni ◽  
Olivier Alata ◽  
Abdellatif El Idrissi ◽  
Brigitte Vannier ◽  
Lynda Zaoui ◽  
...  
Keyword(s):  
Microarray Data ◽  
Data Clustering ◽  
Point Processes ◽  
Marked Point ◽  
Marked Point Processes
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