88 research outputs found
Application of importance sampling to the computation of large deviations in non-equilibrium processes
We present an algorithm for finding the probabilities of rare events in
nonequilibrium processes. The algorithm consists of evolving the system with a
modified dynamics for which the required event occurs more frequently. By
keeping track of the relative weight of phase-space trajectories generated by
the modified and the original dynamics one can obtain the required
probabilities. The algorithm is tested on two model systems of steady-state
particle and heat transport where we find a huge improvement from direct
simulation methods.Comment: 5 pages, 4 figures; some modification
Rare behavior of growth processes via umbrella sampling of trajectories
We compute probability distributions of trajectory observables for reversible and irreversible growth processes. These results reveal a correspondence between reversible and irreversible processes, at particular points in parameter space, in terms of their typical and atypical trajectories. Thus key features of growth processes can be insensitive to the precise form of the rate constants used to generate them, recalling the insensitivity to microscopic details of certain equilibrium behavior. We obtained these results using a sampling method, inspired by the “s-ensemble” large-deviation formalism, that amounts to umbrella sampling in trajectory space. The method is a simple variant of existing approaches, and applies to ensembles of trajectories controlled by the total number of events. It can be used to determine large-deviation rate functions for trajectory observables in or out of equilibrium
Two quantum analogues of Fisher information from a large deviation viewpoint of quantum estimation
We discuss two quantum analogues of Fisher information, symmetric logarithmic
derivative (SLD) Fisher information and Kubo-Mori-Bogoljubov (KMB) Fisher
information from a large deviation viewpoint of quantum estimation and prove
that the former gives the true bound and the latter gives the bound of
consistent superefficient estimators. In another comparison, it is shown that
the difference between them is characterized by the change of the order of
limits.Comment: LaTeX with iopart.cls, iopart12.clo, iopams.st
Systemic Risk and Default Clustering for Large Financial Systems
As it is known in the finance risk and macroeconomics literature,
risk-sharing in large portfolios may increase the probability of creation of
default clusters and of systemic risk. We review recent developments on
mathematical and computational tools for the quantification of such phenomena.
Limiting analysis such as law of large numbers and central limit theorems allow
to approximate the distribution in large systems and study quantities such as
the loss distribution in large portfolios. Large deviations analysis allow us
to study the tail of the loss distribution and to identify pathways to default
clustering. Sensitivity analysis allows to understand the most likely ways in
which different effects, such as contagion and systematic risks, combine to
lead to large default rates. Such results could give useful insights into how
to optimally safeguard against such events.Comment: in Large Deviations and Asymptotic Methods in Finance, (Editors: P.
Friz, J. Gatheral, A. Gulisashvili, A. Jacqier, J. Teichmann) , Springer
Proceedings in Mathematics and Statistics, Vol. 110 2015
Quadratic optimal functional quantization of stochastic processes and numerical applications
In this paper, we present an overview of the recent developments of
functional quantization of stochastic processes, with an emphasis on the
quadratic case. Functional quantization is a way to approximate a process,
viewed as a Hilbert-valued random variable, using a nearest neighbour
projection on a finite codebook. A special emphasis is made on the
computational aspects and the numerical applications, in particular the pricing
of some path-dependent European options.Comment: 41 page
Minimum memory for generating rare events
We classify the rare events of structured, memoryful stochastic processes and use this to analyze sequential and parallel generators for these events. Given a stochastic process, we introduce a method to construct a process whose typical realizations are a given process' rare events. This leads to an expression for the minimum memory required to generate rare events. We then show that the recently discovered classical-quantum ambiguity of simplicity also occurs when comparing the structure of process fluctuations
Effective bandwidth of non-Markovian packet traffic
We demonstrate the application of recent advances in statistical mechanics to
a problem in telecommunication engineering: the assessment of the quality of a
communication channel in terms of rare and extreme events. In particular, we
discuss non-Markovian models for telecommunication traffic in continuous time
and deploy the "cloning" procedure of non-equilibrium statistical mechanics to
efficiently compute their effective bandwidths. The cloning method allows us to
evaluate the performance of a traffic protocol even in the absence of
analytical results, which are often hard to obtain when the dynamics are
non-Markovian
Efficient Radio Transmission with Adaptive and Distributed Beamforming for Intelligent WiMAX
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A Comparative Analysis of the Business Administration Offerings with Special Emphasis upon Marketing in Thirty-two Senior Colleges of Texas with Similar Offerings at North Texas State College, 1954-1955
In this study, a comparative analysis was made of the marketing courses offered in thirty-two senior colleges of Texas including the marketing courses offered at North Texas State College. An analysis was also made to determine what courses in business administration are being offered in the senior colleges in Texas
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