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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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TL;DR: In this article , the authors derived a probabilistic representation of the density of the anomalous process under the Feynman-Kac transform of non-Markov processes.
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TL;DR: In this article, the authors considered one-dimensional directed trap models and assumed that the trapping times are heavy-tailed, and they obtained the inverse of a stable subordinator as scaling limit and proved an aging phenomenon expressed in terms of the generalized arcsine law.
Abstract: We consider one-dimensional directed trap models and suppose that the trapping times are heavy-tailed. We obtain the inverse of a stable subordinator as scaling limit and prove an aging phenomenon expressed in terms of the generalized arcsine law. These results confirm the status of universality described by Ben Arous and \v{C}ern\'y for a large class of graphs.
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TL;DR: In this paper, it was shown that self-decomposability is inherited from subordinator to subordinator in 1-dimensional Brownian motion with drift and in strictly stable cone-parameter convolution semigroups.
Abstract: Extension of two known facts concerning subordination is made. The first fact is that, in subordination of 1-dimensional Brownian motion with drift, selfdecomposability is inherited from subordinator to subordinated. This is extended to subordination of cone-parameter convolution semigroups. The second fact is that, in subordination of strictly stable cone-parameter convolution semigroups on $\mathbb{R}^d$, selfdecomposability is inherited from subordinator to subordinated. This is extended to semi-selfdecomposability.
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TL;DR: In this paper , the authors studied the large-time and small-time asymptotic properties of the spectral heat content for time-changed stable processes, where the time change belongs to a large class of inverse subordinators.
Abstract: We study the large-time and small-time asymptotic behaviors of the spectral heat content for time-changed stable processes, where the time change belongs to a large class of inverse subordinators. For the large-time behavior, the spectral heat content decays polynomially with the decay rate determined by the Laplace exponent of the underlying subordinator, which is in sharp contrast to the exponential decay observed in the case when the time change is a subordinator. On the other hand, the small-time behavior exhibits three different decay regimes, where the decay rate is determined by both the Laplace exponent and the index of the stable process.
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TL;DR: In this paper, the fractional Cauchy problem with Robin condition on the pre-fractal boundary was studied and asymptotic results for the corresponding fractional diffusions with Robin, Neumann and Dirichlet boundary conditions on the fractal domain were obtained.
Abstract: We consider time-changed Brownian motions on random Koch (pre-fractal and fractal) domains where the time change is given by the inverse to a subordinator. In particular, we study the fractional Cauchy problem with Robin condition on the pre-fractal boundary obtaining asymptotic results for the corresponding fractional diffusions with Robin, Neumann and Dirichlet boundary conditions on the fractal domain.