Integration in a dynamical stochastic geometric framework

Giacomo Aletti; Enea G. Bongiorno; Vincenzo Capasso

ESAIM: Probability and Statistics (2012)

  • Volume: 15, page 402-416
  • ISSN: 1292-8100

Abstract

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Motivated by the well-posedness of birth-and-growth processes, a stochastic geometric differential equation and, hence, a stochastic geometric dynamical system are proposed. In fact, a birth-and-growth process can be rigorously modeled as a suitable combination, involving the Minkowski sum and the Aumann integral, of two very general set-valued processes representing nucleation and growth dynamics, respectively. The simplicity of the proposed geometric approach allows to avoid problems of boundary regularities arising from an analytical definition of the front growth. In this framework, growth is generally anisotropic and, according to a mesoscale point of view, is non local, i.e. at a fixed time instant, growth is the same at each point of the space.

How to cite

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Aletti, Giacomo, Bongiorno, Enea G., and Capasso, Vincenzo. "Integration in a dynamical stochastic geometric framework." ESAIM: Probability and Statistics 15 (2012): 402-416. <http://eudml.org/doc/222453>.

@article{Aletti2012,
abstract = { Motivated by the well-posedness of birth-and-growth processes, a stochastic geometric differential equation and, hence, a stochastic geometric dynamical system are proposed. In fact, a birth-and-growth process can be rigorously modeled as a suitable combination, involving the Minkowski sum and the Aumann integral, of two very general set-valued processes representing nucleation and growth dynamics, respectively. The simplicity of the proposed geometric approach allows to avoid problems of boundary regularities arising from an analytical definition of the front growth. In this framework, growth is generally anisotropic and, according to a mesoscale point of view, is non local, i.e. at a fixed time instant, growth is the same at each point of the space. },
author = {Aletti, Giacomo, Bongiorno, Enea G., Capasso, Vincenzo},
journal = {ESAIM: Probability and Statistics},
keywords = {Random closed set; Stochastic geometry; Birth-and-growth process; Set-valued process; Aumann integral; Minkowski sum; random closed set; stochastic geometry; birth-and-growth process; set-valued process},
language = {eng},
month = {1},
pages = {402-416},
publisher = {EDP Sciences},
title = {Integration in a dynamical stochastic geometric framework},
url = {http://eudml.org/doc/222453},
volume = {15},
year = {2012},
}

TY - JOUR
AU - Aletti, Giacomo
AU - Bongiorno, Enea G.
AU - Capasso, Vincenzo
TI - Integration in a dynamical stochastic geometric framework
JO - ESAIM: Probability and Statistics
DA - 2012/1//
PB - EDP Sciences
VL - 15
SP - 402
EP - 416
AB - Motivated by the well-posedness of birth-and-growth processes, a stochastic geometric differential equation and, hence, a stochastic geometric dynamical system are proposed. In fact, a birth-and-growth process can be rigorously modeled as a suitable combination, involving the Minkowski sum and the Aumann integral, of two very general set-valued processes representing nucleation and growth dynamics, respectively. The simplicity of the proposed geometric approach allows to avoid problems of boundary regularities arising from an analytical definition of the front growth. In this framework, growth is generally anisotropic and, according to a mesoscale point of view, is non local, i.e. at a fixed time instant, growth is the same at each point of the space.
LA - eng
KW - Random closed set; Stochastic geometry; Birth-and-growth process; Set-valued process; Aumann integral; Minkowski sum; random closed set; stochastic geometry; birth-and-growth process; set-valued process
UR - http://eudml.org/doc/222453
ER -

References

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