29,946 research outputs found
Scaling and data collapse for the mean exit time of asset prices
We study theoretical and empirical aspects of the mean exit time of financial
time series. The theoretical modeling is done within the framework of
continuous time random walk. We empirically verify that the mean exit time
follows a quadratic scaling law and it has associated a pre-factor which is
specific to the analyzed stock. We perform a series of statistical tests to
determine which kind of correlation are responsible for this specificity. The
main contribution is associated with the autocorrelation property of stock
returns. We introduce and solve analytically both a two-state and a three-state
Markov chain models. The analytical results obtained with the two-state Markov
chain model allows us to obtain a data collapse of the 20 measured MET profiles
in a single master curve.Comment: REVTeX 4, 11 pages, 8 figures, 1 table, submitted for publicatio
Baffling of fluid sloshing in cylindrical tanks Final report
Annular baffle for damping liquid oscillations in partially filled cylindrical tan
Diffusion coefficients for multi-step persistent random walks on lattices
We calculate the diffusion coefficients of persistent random walks on
lattices, where the direction of a walker at a given step depends on the memory
of a certain number of previous steps. In particular, we describe a simple
method which enables us to obtain explicit expressions for the diffusion
coefficients of walks with two-step memory on different classes of one-, two-
and higher-dimensional lattices.Comment: 27 pages, 2 figure
Identification of Coulomb blockade and macroscopic quantum tunneling by noise
The effects of Macroscopic Quantum Tunneling (MQT) and Coulomb Blockade (CB)
in Josephson junctions are of considerable significance both for the
manifestations of quantum mechanics on the macroscopic scale and potential
technological applications. These two complementary effects are shown to be
clearly distinguishable from the associated noise spectra. The current noise is
determined exactly and a rather sharp crossover between flux noise in the MQT
and charge noise in the CB regions is found as the applied voltage is changed.
Related results hold for the voltage noise in current-biased junctions.Comment: 6 pages, 3 figures, epl.cls include
Continuous-Time Random Walks at All Times
Continuous-time random walks (CTRW) play important role in understanding of a
wide range of phenomena. However, most theoretical studies of these models
concentrate only on stationary-state dynamics. We present a new theoretical
approach, based on generalized master equations picture, that allowed us to
obtain explicit expressions for Laplace transforms for all dynamic quantities
for different CTRW models. This theoretical method leads to the effective
description of CTRW at all times. Specific calculations are performed for
homogeneous, periodic models and for CTRW with irreversible detachments. The
approach to stationary states for CTRW is analyzed. Our results are also used
to analyze generalized fluctuations theorem
Effective target arrangement in a deterministic scale-free graph
We study the random walk problem on a deterministic scale-free network, in
the presence of a set of static, identical targets; due to the strong
inhomogeneity of the underlying structure the mean first-passage time (MFPT),
meant as a measure of transport efficiency, is expected to depend sensitively
on the position of targets. We consider several spatial arrangements for
targets and we calculate, mainly rigorously, the related MFPT, where the
average is taken over all possible starting points and over all possible paths.
For all the cases studied, the MFPT asymptotically scales like N^{theta}, being
N the volume of the substrate and theta ranging from (1 - log 2/log3), for
central target(s), to 1, for a single peripheral target.Comment: 8 pages, 5 figure
Universality in Random Walk Models with Birth and Death
Models of random walks are considered in which walkers are born at one
location and die at all other locations with uniform death rate. Steady-state
distributions of random walkers exhibit dimensionally dependent critical
behavior as a function of the birth rate. Exact analytical results for a
hyperspherical lattice yield a second-order phase transition with a nontrivial
critical exponent for all positive dimensions . Numerical studies
of hypercubic and fractal lattices indicate that these exact results are
universal. Implications for the adsorption transition of polymers at curved
interfaces are discussed.Comment: 11 pages, revtex, 2 postscript figure
Slow transport by continuous time quantum walks
Continuous time quantum walks (CTQW) do not necessarily perform better than
their classical counterparts, the continuous time random walks (CTRW). For one
special graph, where a recent analysis showed that in a particular direction of
propagation the penetration of the graph is faster by CTQWs than by CTRWs, we
demonstrate that in another direction of propagation the opposite is true; In
this case a CTQW initially localized at one site displays a slow transport. We
furthermore show that when the CTQW's initial condition is a totally symmetric
superposition of states of equivalent sites, the transport gets to be much more
rapid.Comment: 5 pages, 7 figures, accepted for publication in Phys. Rev.
Escape of a Uniform Random Walk from an Interval
We study the first-passage properties of a random walk in the unit interval
in which the length of a single step is uniformly distributed over the finite
range [-a,a]. For a of the order of one, the exit probabilities to each edge of
the interval and the exit time from the interval exhibit anomalous properties
stemming from the change in the minimum number of steps to escape the interval
as a function of the starting point. As a decreases, first-passage properties
approach those of continuum diffusion, but non-diffusive effects remain because
of residual discreteness effectsComment: 8 pages, 8 figures, 2 column revtex4 forma
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