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Mean reflected BSDE driven by a marked point process and application in insurance risk management
E S A I M: Control, Optimisation and Calculus of VariationsThis paper aims to solve a super-hedging problem along with insurance re-payment under running risk management constraints. The initial endowment for the super-heding problem is characterized by a class of mean reflected backward stochastic differential
Zihao Gu, Yiqing Lin, Xu Kun
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Subsampling Marked Point Processes
1999In this chapter, we assume that {X(t), t ∈ ℝ d } is a homogeneous random field in d dimensions, with d ∈ ℤ+; that is, X(t), t ∈ ℝ d } is a collection of random variables X(t) taking values in an arbitrary state space S, and indexed by the continuous variable t ∈ ℝ d . However, for reasons to be apparent shortly, the probability law of the random field {
Dimitris N. Politis +2 more
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Stationary Marked Point Processes
1987A counting measure on R is a measure m on (R, B) such that $$ {\text{m}}\left( {\text{C}} \right) \in \{ 0,{\text{1}},{\text{ }}.{\text{ }}.{\text{ }}.\infty \} {\text{ for all C}} \in {\text{B}}, $$ (i) $$ {\text{m }} < \left( {\left[ {{\text{a}},{\text{b}}} \right]} \right){\text{ }} < {\text{ }}\infty {\text{ for all a}},{\text{ b ...
François Baccelli, Pierre Brémaud
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Simulating Correlated Marked-point Processes
Journal of Applied Statistics, 2007Abstract The area of marked-point processes is well developed but simulation is still a challenging problem when mark correlations are to be included. In this paper we propose the use of simulated annealing to incorporate the spatial mark correlation into the simulations of correlated marked-point processes.
Xu, C. +4 more
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On Correlations of Marked Point Processes
Mathematische Nachrichten, 1984The paper studies correlations of the marks of marked point processes in \(R^ d\). At first some results of the classical theory of marked point processes are refined. For the case of non-negative marks the mark-sum measure is studied. For a Borel set B it gives the sum of marks of all points in B. Then a mark covariance function is defined which gives
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On Non-simple Marked Point Processes
Annals of the Institute of Statistical Mathematics, 2006The existence and uniqueness of the compensator for simple point processes has long been known. However, relatively little is known about non-simple point processes. Non-simple point processes are not uniquely determined by their conditional intensity and compensator.
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Crater detection based on marked point processes
2010 IEEE International Geoscience and Remote Sensing Symposium, 2010A novel automatic method is developed for the detection of features in planetary images. Although many automatic feature extraction methods have been proposed for for remote sensing images of the Earth, these methods are typically unfeasible for planetary data that generally present low contrast and uneven illumination characteristics.
G. Troglio +3 more
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Some EATA properties for marked point processes
Journal of Applied Probability, 1995We 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.
Kofman, D., Korezlioglu, H.
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Tests for Independence between Marks and Points of a Marked Point Process
Biometrics, 2005Summary A convenient assumption while modeling a marked point process is that the observations (i.e., marks) and the locations (i.e., points) are independent. We propose new graphical and formal testing approaches to test for this assumption. The proposed graphical procedures are easy to obtain and can be used to diagnose the nature and range of ...
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Basics of Stochastic Processes, Point and Marked Point Processes
2015The study of the dynamic performance of engineered systems subject to uncertainty requires the use of tools from stochastic processes. Although stochastic processes have been used extensively in many disciplines (e.g., see [1, 2, 3, 4]), this chapter will focus on the the mathematical background that supports the models presented later in the book. The
Mauricio Sánchez-Silva +1 more
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