New probabilistic methods for physics
We present how a probabilistic model can describe the asymptotic behavior of the iterations, with applications for ODE and approach of some problems in mechanics in $\mathbb{R}^d$.
math.DS↗
arXiv subjects
Guy Cirier
Publications and source records attributed to Guy Cirier.
A probabilistic approach of the Poincar{é}-Bendixon's problem in $\mathbb{R}^d$
We present how a probabilistic model can describe the asymptotic behaviour of the iterations, especially for ODE with an approach of the Poincaré-Bendixon's problem in $\mathbb{R}^d$. On présente un modèle probabiliste pour décrire le comportement asymptotique d'une it{é}ration, en particulier pour les EDO et pour aborder le probl{è}me de Poincaré-Bendixon's dans $\mathbb{R}^d$.
math.DS↗
Linéarisation d'une itération bornée dans Rd par des fonctions de Weierstrass
In this paper, we study an iteration in defined by a diffeomorphism polynomial bounded. Semi invariant curves tend to curves with parametric Weierstrass-Mandelbrot's functions. So, self-similarity and fractal dimension are justified. We apply these results to partial differential calculus. On étudie une itération de Rd dans Rd définie par un difféomorphisme polynomial borné. On montre que les courbes semi invariantes tendent asymptotiquement vers des courbes paramétrées par des fonctions de Weierstrass. Cela justifie les calculs d'échelle d'autosimilarité et de dimension fractale comme le pratiquent des praticiens à partir d'intuitions pertinentes sur des itérations chaotiques. On applique ces résultats au calcul différentiel.
math.DS↗
Bayesian analysis of redistribution policy with a fixed scale
A government has to finance a risk for its population. It shares the charges among the population with a fixed scale based on economic criteria. Various organisms have to collect and to redistribute fairly the subsidies. Under these conditions, when the size of the organisms is varied, the distribution's laws of the criteria are exponential families and criteria are semi linear sufficient statistics.
q-fin.GN↗
Probabilistic and asymptotic methods with the Perron Frobenius's operator
We give a new global presentation of our results on the asymptotic behavior of an iteration. This paper brings many improvements and corrections to our previous preprints on the subject. Among the applications, we use new methods to compute asymptotic results of PDE like Lorenz or Navier-Stokes equations. New questions as the resonance are studied.
math.DS↗
Première approche de la densité d'un opérateur de Perron Frobenius. III - Applications : EDP, EDO, etc
First approach of invariant densities of a Perron Frobenius operator. Asymptotic behaviours of ODE or PDE, as, are most interesting. The associed infinitesimal iteration is. If is partially linear, a random distribution can be asymptotic solution. Among applications, are asymptotic profiles of of Lorenz, Navier Stokes or Hamilton's équations.
math.DS↗