416 research outputs found
The almost-sure asymptotic behavior of the solution to the stochastic heat equation with L\'evy noise
We examine the almost-sure asymptotics of the solution to the stochastic heat
equation driven by a L\'evy space-time white noise. When a spatial point is
fixed and time tends to infinity, we show that the solution develops unusually
high peaks over short time intervals, even in the case of additive noise, which
leads to a breakdown of an intuitively expected strong law of large numbers.
More precisely, if we normalize the solution by an increasing nonnegative
function, we either obtain convergence to , or the limit superior and/or
inferior will be infinite. A detailed analysis of the jumps further reveals
that the strong law of large numbers can be recovered on discrete sequences of
time points increasing to infinity. This leads to a necessary and sufficient
condition that depends on the L\'evy measure of the noise and the growth and
concentration properties of the sequence at the same time. Finally, we show
that our results generalize to the stochastic heat equation with a
multiplicative nonlinearity that is bounded away from zero and infinity.Comment: Forthcoming in The Annals of Probabilit
Randomly Weighted Self-normalized L\'evy Processes
Let be a bivariate L\'evy process, where is a subordinator
and is a L\'evy process formed by randomly weighting each jump of
by an independent random variable having cdf . We investigate the
asymptotic distribution of the self-normalized L\'evy process at 0
and at . We show that all subsequential limits of this ratio at 0
() are continuous for any nondegenerate with finite expectation if
and only if belongs to the centered Feller class at 0 (). We also
characterize when has a non-degenerate limit distribution at 0 and
.Comment: 32 page
Identification of novel stress-responsive biomarkers from gene expression datasets in tomato roots
Published by CSIRO Publishing. This is the Author Accepted Manuscript.
This article may be used for personal use only.Abiotic stresses such as heat, drought or salinity have been widely studied individually. Nevertheless, in the nature and in the field, plants and crops are commonly exposed to a different combination of stresses, which often result in a synergistic response mediated by the activation of several molecular pathways that cannot be inferred from the response to each individual stress. By screening microarray data obtained from different plant species and under different stresses, we identified several conserved stress-responsive genes whose expression was differentially regulated in tomato (Solanum lycopersicum L.) roots in response to one or several stresses. We validated 10 of these genes as reliable biomarkers whose expression levels are related to different signalling pathways involved in adaptive stress responses. In addition, the genes identified in this work could be used as general salt-stress biomarkers to rapidly evaluate the response of salt-tolerant cultivars and wild species for which sufficient genetic information is not yet available
A note on a maximal Bernstein inequality
We show somewhat unexpectedly that whenever a general Bernstein-type maximal
inequality holds for partial sums of a sequence of random variables, a maximal
form of the inequality is also valid.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ304 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
The limit distribution of ratios of jumps and sums of jumps of subordinators
Let be a driftless subordinator, and let denote its jump sequence on interval . Put for the -trimmed subordinator.
In this note we characterize under what conditions the limiting distribution of
the ratios and
exist, as or .Comment: 14 page
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