8,378 research outputs found
Generalized Marshall-Olkin Distributions, and Related Bivariate Aging Properties
National Natural Science Foundation of China [10771090]A class of generalized bivariate Marshall-Olkin distributions, which includes as special cases the Marshall-Olkin bivariate exponential distribution and the Marshall-Olkin type distribution due to Muliere and Scarsini (1987) [19] are examined in this paper. Stochastic comparison results are derived, and bivariate aging properties, together with properties related to evolution of dependence along time, are investigated for this class of distributions. Extensions of results previously presented in the literature are provided as well. (C) 2011 Elsevier Inc. All rights reserved
The percentile residual life up to time t0: ordering and aging properties
Motivated by practical issues, a new stochastic order for random variables is introduced by comparing all their percentile residual life functions until a certain instant. Some interpretations of these stochastic orders are given, and various properties of them are derived. The relationships to other stochastic orders are studied, and also an application in Reliability Theory is described. Finally, we present some characterization results of the decreasing percentile residual life up to time t0 aging notion.Aging notion, Hazard rate, Mean residual life, Percentile residual life, Reliability, Stochastic ordering
Quantum Two-State Dynamics Driven by Stationary Non-Markovian Discrete Noise: Exact Results
We consider the problem of stochastic averaging of a quantum two-state
dynamics driven by non-Markovian, discrete noises of the continuous time random
walk type (multistate renewal processes). The emphasis is put on the proper
averaging over the stationary noise realizations corresponding, e.g., to a
stationary environment. A two state non-Markovian process with an arbitrary
non-exponential distribution of residence times (RTDs) in its states with a
finite mean residence time provides a paradigm. For the case of a two-state
quantum relaxation caused by such a classical stochastic field we obtain the
explicit exact, analytical expression for the averaged Laplace-transformed
relaxation dynamics. In the limit of Markovian noise (implying an exponential
RTD), all previously known results are recovered. We exemplify new more general
results for the case of non-Markovian noise with a biexponential RTD. The
averaged, real-time relaxation dynamics is obtained in this case by numerically
exact solving of a resulting algebraic polynomial problem. Moreover, the case
of manifest non-Markovian noise with an infinite range of temporal
autocorrelation (which in principle is not accessible to any kind of
perturbative treatment) is studied, both analytically (asymptotic long-time
dynamics) and numerically (by a precise numerical inversion of the
Laplace-transformed averaged quantum relaxation).Comment: Chemical Physics, in pres
The percentile residual life up to time t(o): Ordering and aging properties
Motivated by practical issues, a new stochastic order for random variables is introduced by comparing all their percentile residual life functions until a certain instant. Some interpretations of these stochastic orders are given, and various properties of them are derived. The relationships to other stochastic orders are studied and also an application in reliability theory is described. Finally, we present some characterization results of the decreasing percentile residual life up to time to aging notion
Percentile residual life orders
In this paper we study a family of stochastic orders of random variables defined
via the comparison of their percentile residual life functions. Some interpretations
of these stochastic orders are given, and various properties of them are derived.
The relationships to other stochastic orders are also studied. Finally, some
applications in reliability theory and finance are described
Computer Simulations of Supercooled Liquids and Glasses
After a brief introduction to the dynamics of supercooled liquids, we discuss
some of the advantages and drawbacks of computer simulations of such systems.
Subsequently we present the results of computer simulations in which the
dynamics of a fragile glass former, a binary Lennard-Jones system, is compared
to the one of a strong glass former, SiO_2. This comparison gives evidence that
the reason for the different temperature dependence of these two types of glass
formers lies in the transport mechanism for the particles in the vicinity of
T_c, the critical temperature of mode-coupling theory. Whereas the one of the
fragile glass former is described very well by the ideal version of
mode-coupling theory, the one for the strong glass former is dominated by
activated processes. In the last part of the article we review some simulations
of glass formers in which the dynamics below the glass transition temperature
was investigated. We show that such simulations might help to establish a
connection between systems with self generated disorder (e.g. structural
glasses) and quenched disorder (e.g. spin glasses).Comment: 37 pages of Latex, 11 figures, to appear as a Topical Review article
in J. Phys.: Condens. Matte
Multivariate Aging and Archimedean Dependence Structures in High Dimensions
Bivariate aging notions for a vector X of lifetimes based on stochastic comparisons between X and X_t , where X_t is the multivariate residual lifetime after time t > 0, have been studied in Pellerey (2008) under the assumption that the dependence structure in X is described by an Archimedean survival copula. Similar stochastic comparisons between X_t and X_t+s , for all t s > 0, were considered in Mulero and Pellerey (2010). In this article, these results are generalized and extended to the multivariate case. Two illustrative examples are also provided
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