3,737 research outputs found
Propagation of chaos for interacting particles subject to environmental noise
A system of interacting particles described by stochastic differential
equations is considered. As oppopsed to the usual model, where the noise
perturbations acting on different particles are independent, here the particles
are subject to the same space-dependent noise, similar to the (noninteracting)
particles of the theory of diffusion of passive scalars. We prove a result of
propagation of chaos and show that the limit PDE is stochastic and of inviscid
type, as opposed to the case when independent noises drive the different
particles.Comment: Published at http://dx.doi.org/10.1214/15-AAP1120 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Genealogical particle analysis of rare events
In this paper an original interacting particle system approach is developed
for studying Markov chains in rare event regimes. The proposed particle system
is theoretically studied through a genealogical tree interpretation of
Feynman--Kac path measures. The algorithmic implementation of the particle
system is presented. An estimator for the probability of occurrence of a rare
event is proposed and its variance is computed, which allows to compare and to
optimize different versions of the algorithm. Applications and numerical
implementations are discussed. First, we apply the particle system technique to
a toy model (a Gaussian random walk), which permits to illustrate the
theoretical predictions. Second, we address a physically relevant problem
consisting in the estimation of the outage probability due to polarization-mode
dispersion in optical fibers.Comment: Published at http://dx.doi.org/10.1214/105051605000000566 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
NASA Thesaurus supplement: A four part cumulative supplement to the 1988 edition of the NASA Thesaurus (supplement 3)
The four-part cumulative supplement to the 1988 edition of the NASA Thesaurus includes the Hierarchical Listing (Part 1), Access Vocabulary (Part 2), Definitions (Part 3), and Changes (Part 4). The semiannual supplement gives complete hierarchies and accepted upper/lowercase forms for new terms
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