882 research outputs found
Feller Processes: The Next Generation in Modeling. Brownian Motion, L\'evy Processes and Beyond
We present a simple construction method for Feller processes and a framework
for the generation of sample paths of Feller processes. The construction is
based on state space dependent mixing of L\'evy processes.
Brownian Motion is one of the most frequently used continuous time Markov
processes in applications. In recent years also L\'evy processes, of which
Brownian Motion is a special case, have become increasingly popular.
L\'evy processes are spatially homogeneous, but empirical data often suggest
the use of spatially inhomogeneous processes. Thus it seems necessary to go to
the next level of generalization: Feller processes. These include L\'evy
processes and in particular Brownian motion as special cases but allow spatial
inhomogeneities.
Many properties of Feller processes are known, but proving the very existence
is, in general, very technical. Moreover, an applicable framework for the
generation of sample paths of a Feller process was missing. We explain, with
practitioners in mind, how to overcome both of these obstacles. In particular
our simulation technique allows to apply Monte Carlo methods to Feller
processes.Comment: 22 pages, including 4 figures and 8 pages of source code for the
generation of sample paths of Feller processe
Superimposed Renewal Processes in Reliability
This paper reviews the existing literature on the superimposed renewal process, with its foci on probabilistic and statistical properties, statistical inference, and applications in reliability analysis and maintenance policy optimisation. It then proposes future research topics
Exponential ergodicity of the jump-diffusion CIR process
In this paper we study the jump-diffusion CIR process (shorted as JCIR),
which is an extension of the classical CIR model. The jumps of the JCIR are
introduced with the help of a pure-jump L\'evy process . Under
some suitable conditions on the L\'evy measure of , we derive a
lower bound for the transition densities of the JCIR process. We also find some
sufficient condition guaranteeing the existence of a Forster-Lyapunov function
for the JCIR process, which allows us to prove its exponential ergodicity.Comment: 14 page
Signal processing with Levy information
Levy processes, which have stationary independent increments, are ideal for
modelling the various types of noise that can arise in communication channels.
If a Levy process admits exponential moments, then there exists a parametric
family of measure changes called Esscher transformations. If the parameter is
replaced with an independent random variable, the true value of which
represents a "message", then under the transformed measure the original Levy
process takes on the character of an "information process". In this paper we
develop a theory of such Levy information processes. The underlying Levy
process, which we call the fiducial process, represents the "noise type". Each
such noise type is capable of carrying a message of a certain specification. A
number of examples are worked out in detail, including information processes of
the Brownian, Poisson, gamma, variance gamma, negative binomial, inverse
Gaussian, and normal inverse Gaussian type. Although in general there is no
additive decomposition of information into signal and noise, one is led
nevertheless for each noise type to a well-defined scheme for signal detection
and enhancement relevant to a variety of practical situations.Comment: 27 pages. Version to appear in: Proc. R. Soc. London
A Queueing System for Modeling a File Sharing Principle
International audienceWe investigate in this paper the performance of a simple file sharing principle. For this purpose, we consider a system composed of N peers becoming active at exponential random times; the system is initiated with only one server offering the desired file and the other peers after becoming active try to download it. Once the file has been downloaded by a peer, this one immediately becomes a server. To investigate the transient behavior of this file sharing system, we study the instant when the system shifts from a congested state where all servers available are saturated by incoming demands to a state where a growing number of servers are idle. In spite of its apparent simplicity, this queueing model (with a random number of servers) turns out to be quite difficult to analyze. A formulation in terms of an urn and ball model is proposed and corresponding scaling results are derived. These asymptotic results are then compared against simulations
Search for the standard model Higgs boson in the H to ZZ to 2l 2nu channel in pp collisions at sqrt(s) = 7 TeV
A search for the standard model Higgs boson in the H to ZZ to 2l 2nu decay
channel, where l = e or mu, in pp collisions at a center-of-mass energy of 7
TeV is presented. The data were collected at the LHC, with the CMS detector,
and correspond to an integrated luminosity of 4.6 inverse femtobarns. No
significant excess is observed above the background expectation, and upper
limits are set on the Higgs boson production cross section. The presence of the
standard model Higgs boson with a mass in the 270-440 GeV range is excluded at
95% confidence level.Comment: Submitted to JHE
Combined search for the quarks of a sequential fourth generation
Results are presented from a search for a fourth generation of quarks
produced singly or in pairs in a data set corresponding to an integrated
luminosity of 5 inverse femtobarns recorded by the CMS experiment at the LHC in
2011. A novel strategy has been developed for a combined search for quarks of
the up and down type in decay channels with at least one isolated muon or
electron. Limits on the mass of the fourth-generation quarks and the relevant
Cabibbo-Kobayashi-Maskawa matrix elements are derived in the context of a
simple extension of the standard model with a sequential fourth generation of
fermions. The existence of mass-degenerate fourth-generation quarks with masses
below 685 GeV is excluded at 95% confidence level for minimal off-diagonal
mixing between the third- and the fourth-generation quarks. With a mass
difference of 25 GeV between the quark masses, the obtained limit on the masses
of the fourth-generation quarks shifts by about +/- 20 GeV. These results
significantly reduce the allowed parameter space for a fourth generation of
fermions.Comment: Replaced with published version. Added journal reference and DO
Precise measurement of the W-boson mass with the CDF II detector
We have measured the W-boson mass MW using data corresponding to 2.2/fb of
integrated luminosity collected in proton-antiproton collisions at 1.96 TeV
with the CDF II detector at the Fermilab Tevatron collider. Samples consisting
of 470126 W->enu candidates and 624708 W->munu candidates yield the measurement
MW = 80387 +- 12 (stat) +- 15 (syst) = 80387 +- 19 MeV. This is the most
precise measurement of the W-boson mass to date and significantly exceeds the
precision of all previous measurements combined
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