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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 paper, a new class of random composition structures (the ordered analog of Kingman's partition structures) is defined by a regenerative description of component sizes, represented by a process of random sampling of points from an exponential distribution on the positive halfline, and separating the points into clusters by an independent regenerative random set.
Abstract: A new class of random composition structures (the ordered analog of Kingman's partition structures) is defined by a regenerative description of component sizes. Each regenerative composition structure is represented by a process of random sampling of points from an exponential distribution on the positive halfline, and separating the points into clusters by an independent regenerative random set. Examples are composition structures derived from residual allocation models, including one associated with the Ewens sampling formula, and composition structures derived from the zero set of a Brownian motion or Bessel process. We provide characterisation results and formulas relating the distribution of the regenerative composition to the L{\'e}vy parameters of a subordinator whose range is the corresponding regenerative set. In particular, the only reversible regenerative composition structures are those associated with the interval partition of $[0,1]$ generated by excursions of a standard Bessel bridge of dimension $2 - 2 \alpha$ for some $\alpha \in [0,1]$.
10 citations
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TL;DR: In this paper, the authors investigate the windings around the origin of the two-dimensional Markov process (X;L) having the stable L evy process L and its primitive X as coordinates, in the non-trivial case when jLj is not a subordinator.
Abstract: We investigate the windings around the origin of the two-dimensional Markov process (X;L) having the stable L evy process L and its primitive X as coordinates, in the non-trivial case when jLj is not a subordinator. First, we show that these windings have an almost sure limit velocity, extending the result of McKean (1963) in the Brownian case. Second, we evaluate precisely the upper tails of the distribution of the half-winding times, connecting the results of our recent papers Profeta (2014); Profeta and Simon (2014).
10 citations
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TL;DR: In this paper, a multivariate gamma subordinator with gamma margins is introduced to the bivariate variance gamma process, which is a generalization of the bivariance gamma process proposed by Madan and Seneta [7] and calibrated as a price process.
Abstract: In this paper we subordinate a multivariate Brownian motion with independent components by a multivariate gamma subordinator. The resulting process is a generalization of the bivariate variance gamma process proposed by Madan and Seneta [7], mentioned in Cont and Tankov [4] and calibrated in Luciano and Schoutens [5] as a price process. Our main contribution here is to introduce a multivariate subordinator with gamma margins. We investigate the process, determine its Levy triplet and analyze its dependence structure. At the end we propose an exponential Levy price model.
9 citations
TL;DR: In this article, the authors study non-homogeneous versions of the space-fractional and the time-frractional Poisson processes, which can be defined by means of the so-called multistable subordinator (a jump process with non-stationary increments), denoted by H. The authors consider the Poisson process time-changed by H and obtain its explicit distribution and governing equation.
Abstract: The space-fractional and the time-fractional Poisson processes are two well-known models of fractional evolution. They can be constructed as standard Poisson processes with the time variable replaced by a stable subordinator and its inverse, respectively. The aim of this paper is to study non-homogeneous versions of such models, which can be defined by means of the so-called multistable subordinator (a jump process with non-stationary increments), denoted by H. Firstly, we consider the Poisson process time-changed by H and we obtain its explicit distribution and governing equation. Then, by using the right-continuous inverse of H, we define an inhomogeneous analogue of the time-fractional Poisson process.
9 citations
TL;DR: Meerschaert et al. as mentioned in this paper considered the problem of large deviation for the subordinated process Z H ( t ) = W H ( T ( t ), t ≥ 0, where T is the inverse α -stable subordinator.
9 citations