A continuum individual based model of fragmentation: dynamics of correlation functions
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2015)
- Volume: 69, Issue: 2
- ISSN: 0365-1029
Access Full Article
top
Abstract
topHow to cite
topAgnieszka Tanaś. "A continuum individual based model of fragmentation: dynamics of correlation functions." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 69.2 (2015): null. <http://eudml.org/doc/289793>.
@article{AgnieszkaTanaś2015,
abstract = {An individual-based model of an infinite system of point particles in Rd is proposed and studied. In this model, each particle at random produces a finite number of new particles and disappears afterwards. The phase space for this model is the set Γ of all locally finite subsets of Rd. The system's states are probability measures on Γ the Markov evolution of which is described in terms of their correlation functions in a scale of Banach spaces. The existence and uniqueness of solutions of the corresponding evolution equation are proved.},
author = {Agnieszka Tanaś},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Configuration space; individual-based model; birth-and-death process; correlation function; scale of Banach spaces; Ovcyannikov method.},
language = {eng},
number = {2},
pages = {null},
title = {A continuum individual based model of fragmentation: dynamics of correlation functions},
url = {http://eudml.org/doc/289793},
volume = {69},
year = {2015},
}
TY - JOUR
AU - Agnieszka Tanaś
TI - A continuum individual based model of fragmentation: dynamics of correlation functions
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2015
VL - 69
IS - 2
SP - null
AB - An individual-based model of an infinite system of point particles in Rd is proposed and studied. In this model, each particle at random produces a finite number of new particles and disappears afterwards. The phase space for this model is the set Γ of all locally finite subsets of Rd. The system's states are probability measures on Γ the Markov evolution of which is described in terms of their correlation functions in a scale of Banach spaces. The existence and uniqueness of solutions of the corresponding evolution equation are proved.
LA - eng
KW - Configuration space; individual-based model; birth-and-death process; correlation function; scale of Banach spaces; Ovcyannikov method.
UR - http://eudml.org/doc/289793
ER -
References
top- Albeverio, S., Kondratiev, Y., Rockner, M., Analysis and geometry on configuration spaces. J. Funct. Anal. 154 (1998), 444-500.
- Bogoliubov, N., Problems of a dynamical theory in statistical physics, in Studies in Statistical Mechanics, Vol. I (1962), 1-118.
- Boulanouar, M., The asymptotic behavior of a structured cell population, J. Evol. Equ. 11 (3) (2011), 531-552.
- Finkelshtein, D., Around Ovsyannikov’s method, Methods Funct. Anal. Topology 21 (2) (2015), 134-150.
- Finkelshtein, D., Kondratiev, Y., Kozitsky, Y., Glauber dynamics in continuum: A constructive approach to evolution of states, Discrete Contin. Dyn. Syst. 33 (4) (2013), 1431-1450.
- Finkelshtein, D., Kondratiev, Y., Kozitsky, Y., Kutoviy, O., The statistical dynamics of a spatial logistic model and the related kinetic equation, Math. Models Methods Appl. Sci. 25 (2) (2015), 343-370.
- Finkelshtein, D., Kondratiev, Y., Kutoviy, O., Individual based model with competition in spatial ecology, SIAM J. Math. Anal. 41 (2009), 297-317.
- Finkelshtein, D., Kondratiev, Y., Oliveira, M. J., Markov evolution and hierarchical equations in the continuum. I: One-component systems, J. Evol. Equ. 9 (2009), 197-233.
- Garcia, N. L., Kurtz, T. G., Spatial birth and death processes as solutions of stochastic equations, ALEA Lat. Am. J. Probab. Math. Stat. 1 (2006), 281-303.
- Kondratiev, Y., Kuna, T., Harmonic analysis on configuration space. I. General theory, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 5 (2002), 201-233.
- Kondratiev, Y., Kuna, T., Oliveira, M. J., Holomorphic Bogoliubov functionals for interacting particle systems in continuum, J. Funct. Anal. 238 (2006), 375-404.
- Kondratiev, Y., Kutoviy, O., On the metrical properties of the configuration space, Math. Nachr. 279 (2006), 774-783.
- Kondratiev, Y., Kutoviy, O., Pirogov, S., Correlation functions and invariant measures in continuous contact model, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 11 (2008), 231-258.
- Kozitsky, Y., Dynamics of spatial logistic model: finite systems, in Banasiak, J., Bobrowski, A., Lachowicz, M. (eds.) Semigroups of Operators - Theory and Applications, Bedlewo, Poland, October 2013. Springer Proceedings in Mathematics & Statistics 113, 2015, 197-211.
- Lebowitz, J. L., Rubinow, S. I., A theory for the age and generation time distribution of a microbial population, J. Math. Biol. 1 (1974), 17-36.
- Neuhauser, C., Mathematical challenges in spatial ecology, Notices Amer. Math. Soc. 48 (11) (2001), 1304-1314.
- Shanthidevi, C. N., Matsumoto, T., Oharu, S., Nonlinear semigroup approach to age structured proliferating cell population with inherited cycle length, Nonlinear Anal. Real World Appl. 9 (5) (2008), 1905-1917.
- Treves, F., Ovcyannikov Theorem and Hyperdifferential Operators, Instituto de Matem´atica Pura e Aplicada, Conselho Nacional de Pesquisas, Rio de Janeiro, 1968.
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.