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Research talks;Partial Differential Equations;Mathematics in Science and Technology

Inspired by modeling in neurosciences, we here discuss the well-posedness of a networked integrate-and-fire model describing an infinite population of companies which interact with one another through their common statistical distribution. The interaction is of the self-excitatory type as, at any time, the debt of a company increases when some of the others default: precisely, the loss it receives is proportional to the instantaneous proportion of companies that default at the same time. From a mathematical point of view, the coefficient of proportionality, denoted by a, is of great importance as the resulting system is known to blow-up when a takes large values, a blow-up meaning that a macroscopic proportion of companies may default at the same time. In the current talk, we focus on the complementary regime and prove that existence and uniqueness hold in arbitrary time without any blow-up when the excitatory parameter is small enough. Inspired by modeling in neurosciences, we here discuss the well-posedness of a networked integrate-and-fire model describing an infinite population of companies which interact with one another through their common statistical distribution. The interaction is of the self-excitatory type as, at any time, the debt of a company increases when some of the others default: precisely, the loss it receives is proportional to the instantaneous proportion ...

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Documents 35K60 | enregistrements trouvés : 22

Mean-field analysis of an excitatory neuronal network: application to systemic risk modeling? Delarue, François | CIRM Nouveau

Contributions to nonlinear partial differential equationsinternational meeting devoted to... held at the univ. autonoma and univ. complutense of madrid,madrid,dec. 14- 17,1981 Bardos, Claude ; Damlamian, A. ; Diaz, J. I. ; Hernandez, T. | Pitman Advanced Publisher Program 1983 Nouveau

Quasilinear degenerate and nonuniformly elliptic and parabolic equations of seconf order Ivanov, A. V. | Amercian Mathematical Society 1984 Nouveau

Free boundary problems proceedings of the international colloquium,problemes a frontieres libres maubuisson,june 7-16,1984 Bossavit, A. ; Damlamian, A. ; Fremond, M. | Pitman Advanced Publisher Program 1985 Nouveau

Free boundary problems proceedings of the international colloquium,problemes a frontieres libres maubuisson,june 7-16,1984 Bossavit, A. ; Damlamian, A. ; Fremond, M. | Pitman Advanced Publisher Program 1985 Nouveau

Problemes non lineaires Browder, Felix E. | Les Presse de l'Université de Montréal 1966 Nouveau

Free boundary problems :proceedings of the international colloquim on free boundary problems Schwäbisches Bildungszentrum Irsee, West Germany from June 11 to 20, 1987 Hoffmann, K. H. ; Sprekels, J. | Longman Scientific And Technical 1990 Nouveau

Phase transitions and hysteresislectures given at the 3rd session of the Centro Internazionale Matematico Estivo (C.I.M.E.)held in July 13-21 Brokate, M. ; Kenmochi, N. ; Müller, I. ; Visintin, A. | Springer-Verlag 1994 Nouveau

Boundary value problems of mathematical physics XIV :collection of papers Ladyzhenskaya, O. A. | American Mathematical Society 1991 Nouveau

Recent developments in nonlinear partial differential equations :the second symposium on analysis and PDEs#June 7-10 Danielli, Donatella | Amercian Mathematical Society 2007 Nouveau

The boundary value problems of mathematical physics Ladyzhenskaya, O. A. | Springer-Verlag 1985 Nouveau

Instability, nonexistence and weighted energy methods in fluid dynamics and related theories Straughan, B. | 1982 Nouveau

Infinite-dimensional dynamical systems in mechanics and physics Temam, Roger | Springer-Verlag 1988 Nouveau

Boundary value problems and markov processes Taira, Kazuaki | Springer-Verlag 1991 Nouveau

Nonlinear equations in the applied sciences Ames, William F. ; Rogers, C. A. | Academic Press Inc. 1992 Nouveau

Analyse mathématique de modèles non linéaires de l Gagneux, Gérard ; Madaune-Tort, Monique | Springer 1996 Nouveau

Proceedings of the St. Petersburg mathematical society. Vol. VIII Uraltseva, N. N. | American Mathematical Society 2002 Nouveau

Eléments d'analyse pour l'étude de quelques modèles d'écoulements de fluides visqueux incompressibles Boyer, Franck ; Fabrie, Pierre | Springer 2006 Nouveau

Infinite-Dimensional Dynamical Systems in Mechanics and Physics Temam, Roger | Springer 1997 Nouveau

Optimal Control of Partial Differential Equations : Theory, Methods and Applications Troltzsch, Fredi ; Sprekels, J. | American Mathematical Society 2010 Nouveau

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Contributions to nonlinear partial differential equations
international meeting devoted to... held at the univ. autonoma and univ. complutense of madrid,madrid,dec. 14- 17,1981 Bardos, Claude ; Damlamian, A. ; Diaz, J. I. ; Hernandez, T. | Pitman Advanced Publisher Program 1983 Nouveau

Free boundary problems
proceedings of the international colloquium,problemes a frontieres libres maubuisson,june 7-16,1984 Bossavit, A. ; Damlamian, A. ; Fremond, M. | Pitman Advanced Publisher Program 1985 Nouveau

Free boundary problems
proceedings of the international colloquium,problemes a frontieres libres maubuisson,june 7-16,1984 Bossavit, A. ; Damlamian, A. ; Fremond, M. | Pitman Advanced Publisher Program 1985 Nouveau

Free boundary problems :
proceedings of the international colloquim on free boundary problems Schwäbisches Bildungszentrum Irsee, West Germany from June 11 to 20, 1987 Hoffmann, K. H. ; Sprekels, J. | Longman Scientific And Technical 1990 Nouveau

Phase transitions and hysteresis
lectures given at the 3rd session of the Centro Internazionale Matematico Estivo (C.I.M.E.)
held in July 13-21 Brokate, M. ; Kenmochi, N. ; Müller, I. ; Visintin, A. | Springer-Verlag 1994 Nouveau

Boundary value problems of mathematical physics XIV :
collection of papers Ladyzhenskaya, O. A. | American Mathematical Society 1991 Nouveau

Recent developments in nonlinear partial differential equations :
the second symposium on analysis and PDEs#June 7-10 Danielli, Donatella | Amercian Mathematical Society 2007 Nouveau