23,455 research outputs found
Fluctuations of the front in a one-dimensional model for the spread of an infection
We study the following microscopic model of infection or epidemic reaction:
red and blue particles perform independent nearest-neighbor continuous-time
symmetric random walks on the integer lattice with jump rates
for red particles and for blue particles, the interaction rule
being that blue particles turn red upon contact with a red particle. The
initial condition consists of i.i.d. Poisson particle numbers at each site,
with particles at the left of the origin being red, while particles at the
right of the origin are blue. We are interested in the dynamics of the front,
defined as the rightmost position of a red particle. For the case ,
Kesten and Sidoravicius established that the front moves ballistically, and
more precisely that it satisfies a law of large numbers. Their proof is based
on a multi-scale renormalization technique, combined with approximate
sub-additivity arguments. In this paper, we build a renewal structure for the
front propagation process, and as a corollary we obtain a central limit theorem
for the front when . Moreover, this result can be extended to the case
where , up to modifying the dynamics so that blue particles turn red
upon contact with a site that has previously been occupied by a red particle.
Our approach extends the renewal structure approach developed by Comets,
Quastel and Ram\'{{\i}}rez for the so-called frog model, which corresponds to
the case.Comment: Published at http://dx.doi.org/10.1214/15-AOP1034 in the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
When each continuous operator is regular, II
The following theorem is essentially due to L.~Kantorovich and B. Vulikh and
it describes one of the most important classes of Banach lattices between which
each continuous operator is regular. {\bf Theorem 1.1.} {\sl Let be an
arbitrary L-space and be an arbitrary Banach lattice with Levi norm. Then
that is, every continuous operator
from to is regular.}
In spite of the importance of this theorem it has not yet been determined to
what extent the Levi condition is essential for the validity of equality
. Our main aim in this work is to prove a converse to this theorem by
showing that for a Dedekind complete the Levi condition is necessary for
the validity of .
As a sample of other results we mention the following. {\bf Theorem~3.6.}
{\sl For a Banach lattice the following are equivalent: {\rm (a)} is
Dedekind complete; {\rm (b)} For all Banach lattices , the space is a Dedekind complete vector lattice; {\rm (c)} For all L-spaces
, the space is a vector lattice.
Utility of correlation techniques in gravity and magnetic interpretation
Two methods of quantitative combined analysis, internal correspondence and clustering, are presented. Model studies are used to illustrate implementation and interpretation procedures of these methods, particularly internal correspondence. Analysis of the results of applying these methods to data from the midcontinent and a transcontinental profile show they can be useful in identifying crustal provinces, providing information on horizontal and vertical variations of physical properties over province size zones, validating long wave-length anomalies, and isolating geomagnetic field removal problems. Thus, these techniques are useful in considering regional data acquired by satellites
A Characterization for Decidable Separability by Piecewise Testable Languages
The separability problem for word languages of a class by
languages of a class asks, for two given languages and
from , whether there exists a language from that
includes and excludes , that is, and . In this work, we assume some mild closure properties for
and study for which such classes separability by a piecewise
testable language (PTL) is decidable. We characterize these classes in terms of
decidability of (two variants of) an unboundedness problem. From this, we
deduce that separability by PTL is decidable for a number of language classes,
such as the context-free languages and languages of labeled vector addition
systems. Furthermore, it follows that separability by PTL is decidable if and
only if one can compute for any language of the class its downward closure wrt.
the scattered substring ordering (i.e., if the set of scattered substrings of
any language of the class is effectively regular).
The obtained decidability results contrast some undecidability results. In
fact, for all (non-regular) language classes that we present as examples with
decidable separability, it is undecidable whether a given language is a PTL
itself.
Our characterization involves a result of independent interest, which states
that for any kind of languages and , non-separability by PTL is
equivalent to the existence of common patterns in and
Prudent Monetary Policy and Cautious Prediction of the Output Gap
Using the results of risk-adjusted linear-quadratic-Gaussian optimal control with perfect and imperfect observation of the economy, we obtain prudent Taylor rules for monetary policies and also allow for imperfect information and cautious Kalman filters. A prudent central bank adjusts the nominal interest rate more aggressively to changes in the inflation gap, especially if the volatility of cost-push shocks is large. If the interest rate impacts the output gap after a lag, the interest also responds to the output gap, especially with strong persistence in aggregate demand. Prudence pushes up this reaction coefficient as well. If data are poor and appear with a lag, a prudent central bank responds less strongly to new measurements of the output gap. However, prudence attenuates this policy reaction and biases the prediction of the output gap upwards, particularly if output targeting is important. Finally, prudence requires an extra upward (downward) bias in its estimate of the output gap before it feeds into the policy rule if inflation is above (below) target. This reinforces nominal interest rate reactions. A general lesson is that prudent predictions are neither efficient nor unbiased.prudence, optimal monetary policy, Taylor rules, measurement errors, prediction
Compactness in Spaces of Inner Regular Measures and a General Portmanteau Lemma
This paper may be understood as a continuation of Topsøe’s seminal paper ([16]) to characterize, within an abstract setting, compact subsets of finite inner regular measures w.r.t. the weak topology. The new aspect is that neither assumptions on compactness of the inner approximating lattices nor nonsequential continuity properties for the measures will be imposed. As a providing step also a generalization of the classical Portmanteau lemma will be established. The obtained characterizations of compact subsets w.r.t. the weak topology encompass several known ones from literature. The investigations rely basically on the inner extension theory for measures which has been systemized recently by König ([8], [10],[12]).Inner Premeasures, Weak Topology, Generalized Portmanteau Lemma.
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