Browsing by Subject "math.DS"
Now showing items 1-13 of 13
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A Large Deviation Approach to Posterior Consistency in Dynamical Systems
In this paper, we provide asymptotic results concerning (generalized) Bayesian inference for certain dynamical systems based on a large deviation approach. Given a sequence of observations $y$, a class of model ... -
Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials
(2017-11-30)We study Langevin dynamics of $N$ particles on $R^d$ interacting through a singular repulsive potential, e.g.~the well-known Lennard-Jones type, and show that the system converges to the unique invariant Gibbs measure ... -
Geometric ergodicity of Langevin dynamics with Coulomb interactions
This paper is concerned with the long time behavior of Langevin dynamics of {\em Coulomb gases} in $\mathbf{R}^d$ with $d\geq 2$, that is a second order system of Brownian particles driven by an external force and ... -
Higher order asymptotics for large deviations -- Part I
For sequences of non-lattice weakly dependent random variables, we obtain asymptotic expansions for Large Deviation Principles. These expansions, commonly referred to as strong large deviation results, are in the spirit ... -
Noise-induced strong stabilization
We consider a 2-dimensional stochastic differential equation in polar coordinates depending on several parameters. We show that if these parameters belong to a specific regime then the deterministic system explodes ... -
On the mean-field limit for the Vlasov-Poisson-Fokker-Planck system
We devise and study a random particle blob method for approximating the Vlasov-Poisson-Fokkker-Planck (VPFP) equations by a $N$-particle system subject to the Brownian motion in $\mathbb{R}^3$ space. More precisely, we show ... -
Propagation of Fluctuations in Biochemical Systems, II: Nonlinear Chains
We consider biochemical reaction chains and investigate how random external fluctuations, as characterized by variance and coefficient of variation, propagate down the chains. We perform such a study under the assumption ... -
Random Splitting of Fluid Models: Ergodicity and Convergence
(2022-01-17) -
Scaling and Saturation in Infinite-Dimensional Control Problems with Applications to Stochastic Partial Differential Equations
(2017-07-27)We establish the dual notions of scaling and saturation from geometric control theory in an infinite-dimensional setting. This generalization is applied to the low-mode control problem in a number of concrete nonlinear partial ... -
Scaling limits of a model for selection at two scales
(2015)The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. ... -
Singularities of invariant densities for random switching between two linear ODEs in 2D
We consider a planar dynamical system generated by two stable linear vector fields with distinct fixed points and random switching between them. We characterize singularities of the invariant density in terms of ... -
Smooth invariant densities for random switching on the torus
(2017-08-30)We consider a random dynamical system obtained by switching between the flows generated by two smooth vector fields on the 2d-torus, with the random switchings happening according to a Poisson process. Assuming that the ...
