2,873 research outputs found
Parabolic Harnack Inequality and Local Limit Theorem for Percolation Clusters
We consider the random walk on supercritical percolation clusters in the
d-dimensional Euclidean lattice. Previous papers have obtained Gaussian heat
kernel bounds, and a.s. invariance principles for this process. We show how
this information leads to a parabolic Harnack inequality, a local limit theorem
and estimates on the Green's function.Comment: 29 page
Existence and space-time regularity for stochastic heat equations on p.c.f. fractals
We define linear stochastic heat equations (SHE) on p.c.f.s.s. sets equipped
with regular harmonic structures. We show that if the spectral dimension of the
set is less than two, then function-valued "random-field" solutions to these
SPDEs exist and are jointly H\"older continuous in space and time. We calculate
the respective H\"older exponents, which extend the well-known results on the
H\"older exponents of the solution to SHE on the unit interval. This shows that
the "curse of dimensionality" of the SHE on depends not on the
geometric dimension of the ambient space but on the analytic properties of the
operator through the spectral dimension. To prove these results we establish
generic continuity theorems for stochastic processes indexed by these
p.c.f.s.s. sets that are analogous to Kolmogorov's continuity theorem. We also
investigate the long-time behaviour of the solutions to the fractal SHEs
A Reflected Moving Boundary Problem Driven by Space-Time White Noise
We study a system of two reflected SPDEs which share a moving boundary. The
equations describe competition at an interface and are motivated by the
modelling of the limit order book in financial markets. The derivative of the
moving boundary is given by a function of the two SPDEs in their relative
frames. We prove existence and uniqueness for the equations until blow-up, and
show that the solution is global when the boundary speed is bounded. We also
derive the expected H\"older continuity for the process and hence for the
derivative of the moving boundary. Both the case when the spatial domains are
given by fixed finite distances from the shared boundary, and when the spatial
domains are the semi-infinite intervals on either side of the shared boundary
are considered. In the second case, our results require us to further develop
the known theory for reflected SPDEs on infinite spatial domains by extending
the uniqueness theory and establishing the local H\"older continuity of the
solutions
Monte Carlo methods for the valuation of multiple exercise options
We discuss Monte Carlo methods for valuing options with multiple exercise features in discrete time. By extending the recently developed duality ideas for American option pricing we show how to obtain estimates on the prices of such options using Monte Carlo techniques. We prove convergence of our approach and estimate the error. The methods are applied to options in the energy and interest rate derivative markets
Mice that gorged during dietary restriction increased foraging related behaviors and differed in their macronutrient preference when released from restriction
This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ) and either DOI or URL of the article must be cited. Funding This work was funded by the University of Aberdeen. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Acknowledgements We are grateful for the assistance provided by Caitlin Begley, the animal house staff at the University of Aberdeen, Paula Redman and Nick Fewkes.Peer reviewedPublisher PD
Cleaning sky survey databases using Hough Transform and Renewal String approaches
Large astronomical databases obtained from sky surveys such as the
SuperCOSMOS Sky Survey (SSS) invariably suffer from spurious records coming
from artefactual effects of the telescope, satellites and junk objects in orbit
around earth and physical defects on the photographic plate or CCD. Though
relatively small in number these spurious records present a significant problem
in many situations where they can become a large proportion of the records
potentially of interest to a given astronomer. Accurate and robust techniques
are needed for locating and flagging such spurious objects, and we are
undertaking a programme investigating the use of machine learning techniques in
this context. In this paper we focus on the four most common causes of unwanted
records in the SSS: satellite or aeroplane tracks, scratches, fibres and other
linear phenomena introduced to the plate, circular halos around bright stars
due to internal reflections within the telescope and diffraction spikes near to
bright stars. Appropriate techniques are developed for the detection of each of
these. The methods are applied to the SSS data to develop a dataset of spurious
object detections, along with confidence measures, which can allow these
unwanted data to be removed from consideration. These methods are general and
can be adapted to other astronomical survey data.Comment: Accepted for MNRAS. 17 pages, latex2e, uses mn2e.bst, mn2e.cls,
md706.bbl, shortbold.sty (all included). All figures included here as low
resolution jpegs. A version of this paper including the figures can be
downloaded from http://www.anc.ed.ac.uk/~amos/publications.html and more
details on this project can be found at
http://www.anc.ed.ac.uk/~amos/sattrackres.htm
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