8,804 research outputs found
Online Sequential Monte Carlo smoother for partially observed stochastic differential equations
This paper introduces a new algorithm to approximate smoothed additive
functionals for partially observed stochastic differential equations. This
method relies on a recent procedure which allows to compute such approximations
online, i.e. as the observations are received, and with a computational
complexity growing linearly with the number of Monte Carlo samples. This online
smoother cannot be used directly in the case of partially observed stochastic
differential equations since the transition density of the latent data is
usually unknown. We prove that a similar algorithm may still be defined for
partially observed continuous processes by replacing this unknown quantity by
an unbiased estimator obtained for instance using general Poisson estimators.
We prove that this estimator is consistent and its performance are illustrated
using data from two models
Lyapunov functionals for boundary-driven nonlinear drift-diffusions
We exhibit a large class of Lyapunov functionals for nonlinear
drift-diffusion equations with non-homogeneous Dirichlet boundary conditions.
These are generalizations of large deviation functionals for underlying
stochastic many-particle systems, the zero range process and the
Ginzburg-Landau dynamics, which we describe briefly. As an application, we
prove linear inequalities between such an entropy-like functional and its
entropy production functional for the boundary-driven porous medium equation in
a bounded domain with positive Dirichlet conditions: this implies exponential
rates of relaxation related to the first Dirichlet eigenvalue of the domain. We
also derive Lyapunov functions for systems of nonlinear diffusion equations,
and for nonlinear Markov processes with non-reversible stationary measures
On the -limit for a non-uniformly bounded sequence of two phase metric functionals
In this study we consider the -limit of a highly oscillatory
Riemannian metric length functional as its period tends to 0. The metric
coefficient takes values in either or where and . We
find that for a large class of metrics, in particular those metrics whose
surface of discontinuity forms a differentiable manifold, the -limit
exists, as in the uniformly bounded case. However, when one attempts to
determine the -limit for the corresponding boundary value problem, the
existence of the -limit depends on the value of . Specifically, we
show that the power is critical in that the -limit exists for , whereas it ceases to exist for . The results here have
applications in both nonlinear optics and the effective description of a
Hamiltonian particle in a discontinuous potential.Comment: 31 pages, 1 figure. Submitte
- …