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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TL;DR: In this article, the authors investigated the asymptotic distribution of the self-normalized Levy process U t / V t at 0 and at ∞ and showed that all subsequential limits of this ratio at 0 ( ∞ ) are continuous for any nondegenerate F with finite expectation if and only if V t belongs to the centered Feller class.
7 citations
TL;DR: A Monte Carlo method is developed for simulating discrete time random walks with Sibuya power law waiting times, providing another approximate solution of the fractional subdiffusion equation.
7 citations
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TL;DR: In this article, the authors established a link between the distribution of an exponential functional I and the undershoots of a subordinator, which was given in terms of the associated harmonic potential measure.
Abstract: We establish a link between the distribution of an exponential functional I and the undershoots of a subordinator, which is given in terms of the associated harmonic potential measure. This allows us to give a necessary and sufficient condition in terms of the L\'evy measure for the exponential functional to be multiplicative infinitely divisible. We then provide a formula for the moment generating function of an exponential functional $I$ and the so called remainder random variable $R$ associated to it. We provide a realization of the remainder random variable $R$ as an infinite product involving independent last position random variables of the subordinator. Some properties of harmonic measures are obtained and some examples are provided.
7 citations
TL;DR: In this paper, the authors established large deviation results for the process Z H and its supremum process and also gave asymptotic properties of the tail probability of the supremum processes.
7 citations
TL;DR: In this article, the authors studied the asymptotic behavior of the heat kernels of non-local (partial and pseudo-differential) equations with fractional operators in time and space.
Abstract: We study the asymptotic behaviour of the fundamental solutions (heat kernels) of non-local (partial and pseudo differential) equations with fractional operators in time and space. In particular, we obtain exact asymptotic formulas for the heat kernels of time-changed Brownian motions and Cauchy processes.
7 citations