8,982 research outputs found
- and - Relaxation Dynamics of a fragile plastic crystal
We present a thorough dielectric investigation of the relaxation dynamics of
plastic crystalline Freon112, which exhibits freezing of the orientational
degrees of freedom into a glassy crystal below 90 K. Among other plastic
crystals, Freon112 stands out by being relatively fragile within Angell's
classification scheme and by showing an unusually strong -relaxation.
Comparing the results to those on Freon112a, having only a single molecular
conformation, points to the importance of the presence of two molecular
conformations in Freon112 for the explanation of its unusual properties.Comment: 17 pages, 6 figure
Distributional properties of exponential functionals of Levy processes
We study the distribution of the exponential functional
I(\xi,\eta)=\int_0^{\infty} \exp(\xi_{t-}) \d \eta_t, where and
are independent L\'evy processes. In the general setting using the theories of
Markov processes and Schwartz distributions we prove that the law of this
exponential functional satisfies an integral equation, which generalizes
Proposition 2.1 in Carmona et al "On the distribution and asymptotic results
for exponential functionals of Levy processes". In the special case when
is a Brownian motion with drift we show that this integral equation leads to an
important functional equation for the Mellin transform of , which
proves to be a very useful tool for studying the distributional properties of
this random variable. For general L\'evy process ( being Brownian
motion with drift) we prove that the exponential functional has a smooth
density on , but surprisingly the second derivative at zero
may fail to exist. Under the additional assumption that has some positive
exponential moments we establish an asymptotic behaviour of \p(I(\xi,\eta)>x)
as , and under similar assumptions on the negative exponential
moments of we obtain a precise asympotic expansion of the density of
as . Under further assumptions on the L\'evy process
one is able to prove much stronger results about the density of the
exponential functional and we illustrate some of the ideas and techniques for
the case when has hyper-exponential jumps.Comment: In this version we added a remark after Theorem 1 about extra
conditions required for validity of equation (2.3
The extended hypergeometric class of L\'evy processes
With a view to computing fluctuation identities related to stable processes,
we review and extend the class of hypergeometric L\'evy processes explored in
Kuznetsov and Pardo (arXiv:1012.0817). We give the Wiener-Hopf factorisation of
a process in the extended class, and characterise its exponential functional.
Finally, we give three concrete examples arising from transformations of stable
processes.Comment: 22 page
Authoring courses with rich adaptive sequencing for IMS learning design
This paper describes the process of translating an adaptive sequencing strategy designed using Sequencing Graphs to the semantics of IMS Learning Design. The relevance of this contribution is twofold. First, it combines the expressive power and flexibility of Sequencing Graphs, and the interoperability capabilities of IMS. Second, it shows some important limitations of IMS specifications (focusing on Learning Design) for the sequencing of learning activities
A Wiener--Hopf Monte Carlo simulation technique for L\'{e}vy processes
We develop a completely new and straightforward method for simulating the
joint law of the position and running maximum at a fixed time of a general
L\'{e}vy process with a view to application in insurance and financial
mathematics. Although different, our method takes lessons from Carr's so-called
"Canadization" technique as well as Doney's method of stochastic bounds for
L\'{e}vy processes; see Carr [Rev. Fin. Studies 11 (1998) 597--626] and Doney
[Ann. Probab. 32 (2004) 1545-1552]. We rely fundamentally on the Wiener-Hopf
decomposition for L\'{e}vy processes as well as taking advantage of recent
developments in factorization techniques of the latter theory due to Vigon
[Simplifiez vos L\'{e}vy en titillant la factorization de Wiener-Hopf (2002)
Laboratoire de Math\'{e}matiques de L'INSA de Rouen] and Kuznetsov [Ann. Appl.
Probab. 20 (2010) 1801--1830]. We illustrate our Wiener--Hopf Monte Carlo
method on a number of different processes, including a new family of L\'{e}vy
processes called hypergeometric L\'{e}vy processes. Moreover, we illustrate the
robustness of working with a Wiener--Hopf decomposition with two extensions.
The first extension shows that if one can successfully simulate for a given
L\'{e}vy processes then one can successfully simulate for any independent sum
of the latter process and a compound Poisson process. The second extension
illustrates how one may produce a straightforward approximation for simulating
the two-sided exit problem.Comment: Published in at http://dx.doi.org/10.1214/10-AAP746 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
An exploratory canonical analysis approach for multinomial populations based on the -divergence measure
summary:In this paper we consider an exploratory canonical analysis approach for multinomial population based on the -divergence measure. We define the restricted minimum -divergence estimator, which is seen to be a generalization of the restricted maximum likelihood estimator. This estimator is then used in -divergence goodness-of-fit statistics which is the basis of two new families of statistics for solving the problem of selecting the number of significant correlations as well as the appropriateness of the model
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