6,383 research outputs found
Temporal and Spatial Data Mining with Second-Order Hidden Models
In the frame of designing a knowledge discovery system, we have developed
stochastic models based on high-order hidden Markov models. These models are
capable to map sequences of data into a Markov chain in which the transitions
between the states depend on the \texttt{n} previous states according to the
order of the model. We study the process of achieving information extraction
fromspatial and temporal data by means of an unsupervised classification. We
use therefore a French national database related to the land use of a region,
named Teruti, which describes the land use both in the spatial and temporal
domain. Land-use categories (wheat, corn, forest, ...) are logged every year on
each site regularly spaced in the region. They constitute a temporal sequence
of images in which we look for spatial and temporal dependencies. The temporal
segmentation of the data is done by means of a second-order Hidden Markov Model
(\hmmd) that appears to have very good capabilities to locate stationary
segments, as shown in our previous work in speech recognition. Thespatial
classification is performed by defining a fractal scanning ofthe images with
the help of a Hilbert-Peano curve that introduces atotal order on the sites,
preserving the relation ofneighborhood between the sites. We show that the
\hmmd performs aclassification that is meaningful for the agronomists.Spatial
and temporal classification may be achieved simultaneously by means of a 2
levels \hmmd that measures the \aposteriori probability to map a temporal
sequence of images onto a set of hidden classes
Stochastic integral representation and regularity of the density for the Exit measure of super-Brownian motion
This paper studies the regularity properties of the density of the exit
measure for super-Brownian motion with (1+\beta)-stable branching mechanism. It
establishes the continuity of the density in dimension d=2 and the
unboundedness of the density in all other dimensions where the density exists.
An alternative description of the exit measure and its density is also given
via a stochastic integral representation. Results are applied to the
probabilistic representation of nonnegative solutions of the partial
differential equation \Delta u=u^{1+\beta}.Comment: Published at http://dx.doi.org/10.1214/009117904000000612 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Conditioned Brownian trees
We consider a Brownian tree consisting of a collection of one-dimensional
Brownian paths started from the origin, whose genealogical structure is given
by the Continuum Random Tree (CRT). This Brownian tree may be generated from
the Brownian snake driven by a normalized Brownian excursion, and thus yields a
convenient representation of the so-called Integrated Super-Brownian Excursion
(ISE), which can be viewed as the uniform probability measure on the tree of
paths. We discuss different approaches that lead to the definition of the
Brownian tree conditioned to stay on the positive half-line. We also establish
a Verwaat-like theorem showing that this conditioned Brownian tree can be
obtained by re-rooting the unconditioned one at the vertex corresponding to the
minimal spatial position. In terms of ISE, this theorem yields the following
fact: Conditioning ISE to put no mass on and letting
go to 0 is equivalent to shifting the unconditioned ISE to the right
so that the left-most point of its support becomes the origin. We derive a
number of explicit estimates and formulas for our conditioned Brownian trees.
In particular, the probability that ISE puts no mass on
is shown to behave like when goes to 0. Finally,
for the conditioned Brownian tree with a fixed height , we obtain a
decomposition involving a spine whose distribution is absolutely continuous
with respect to that of a nine-dimensional Bessel process on the time interval
, and Poisson processes of subtrees originating from this spine.Comment: 42 page
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