138 research outputs found
On ergodicity of some Markov processes
We formulate a criterion for the existence and uniqueness of an invariant
measure for a Markov process taking values in a Polish phase space. In
addition, weak- ergodicity, that is, the weak convergence of the ergodic
averages of the laws of the process starting from any initial distribution, is
established. The principal assumptions are the existence of a lower bound for
the ergodic averages of the transition probability function and its local
uniform continuity. The latter is called the e-property. The general result is
applied to solutions of some stochastic evolution equations in Hilbert spaces.
As an example, we consider an evolution equation whose solution describes the
Lagrangian observations of the velocity field in the passive tracer model. The
weak- mean ergodicity of the corresponding invariant measure is used to
derive the law of large numbers for the trajectory of a tracer.Comment: Published in at http://dx.doi.org/10.1214/09-AOP513 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Evaluation of Hashing Methods Performance on Binary Feature Descriptors
In this paper we evaluate performance of data-dependent hashing methods on
binary data. The goal is to find a hashing method that can effectively produce
lower dimensional binary representation of 512-bit FREAK descriptors. A
representative sample of recent unsupervised, semi-supervised and supervised
hashing methods was experimentally evaluated on large datasets of labelled
binary FREAK feature descriptors
Principal eigenvalue of the fractional Laplacian with a large incompressible drift
We add a divergence-free drift with increasing magnitude to the fractional
Laplacian on a bounded smooth domain, and discuss the behavior of the principal
eigenvalue for the Dirichlet problem. The eigenvalue remains bounded if and
only if the drift has non-trivial first integrals in the domain of the
quadratic form of the fractional Laplacian.Comment: 19 page
On stationarity of Lagrangian observations of passive tracer velocity in a compressible environment
We study the transport of a passive tracer particle in a steady strongly
mixing flow with a nonzero mean velocity. We show that there exists a
probability measure under which the particle Lagrangian velocity process is
stationary. This measure is absolutely continuous with respect to the
underlying probability measure for the Eulerian flow.Comment: Published at http://dx.doi.org/10.1214/105051604000000945 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
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