Topic
Subordinator
About: Subordinator is a research topic. Over the lifetime, 771 publications have been published within this topic receiving 15383 citations.
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12 May 2003
TL;DR: In this article, it was shown that the past and future of halfplane Brownian motion at certain cutpoints are independent of each other after a conformal transformation, and that the pieces between cutpoints form a Poisson process with respect to a local time.
Abstract: We show that the past and future of half-plane Brownian motion at certain cutpoints are independent of each other after a conformal transformation Like in Ito's excursion theory, the pieces between cutpoints form a Poisson process with respect to a local time The size of the path as a function of this local time is a stable subordinator whose index is given by the exponent of the probability that a stretch of the path has no cutpoint The index is computed and equals 1/2
22 citations
TL;DR: In this article, the effect of multiple sources of degradation on deteriorating systems is modeled as a general increasing Levy process (i.e., a subordinator), which is a process with independent, stationary and non-negative increments, and the results demonstrate the generality, versatility, efficiency and accuracy of the proposed Levy degradation framework.
22 citations
TL;DR: In this paper, the authors studied the convergence rate of a Markov process to its invariant measure with a subordinator and the corresponding Bernstein function and showed that subordination can dramatically change the speed of convergence to equilibrium.
Abstract: We are interested in the rate of convergence of a subordinate Markov process to its invariant measure. Given a subordinator and the corresponding Bernstein function (Laplace exponent) we characterize the convergence rate of the subordinate Markov process; the key ingredients are the rate of convergence of the original process and the (inverse of the) Bernstein function. At a technical level, the crucial point is to bound three types of moments (sub-exponential, algebraic and logarithmic) for subordinators as time $t$ tends to infinity. At the end we discuss some concrete models and we show that subordination can dramatically change the speed of convergence to equilibrium.
21 citations
Posted Content•
TL;DR: In this article, the Gamma subordinator is represented as a Krein functional of Brownian motion, using the known representations for stable subordinators and Esscher transforms, which are used to obtain Krein representations of the subordinators which govern the two parameter Poisson Dirichlet family of distributions.
Abstract: We give a representation of the Gamma subordinator as a Krein functional of Brownian motion, using the known representations for stable subordinators and Esscher transforms. In particular, we have obtained Krein representations of the subordinators which govern the two parameter Poisson-Dirichlet family of distributions.
21 citations
Posted Content•
TL;DR: In this article, the fractional Poisson process was generated by subordinating the standard Poisson processes to the inverse stable subordinator, based on application of the Laplace transform with respect to both arguments of the evolving probability densities.
Abstract: We generate the fractional Poisson process by subordinating the standard Poisson process to the inverse stable subordinator. Our analysis is based on application of the Laplace transform with respect to both arguments of the evolving probability densities.
21 citations