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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, the authors present an exact sampling method for the first passage event of a Levy process, which is based on several distributional properties that appear to be new, such as bounded variation and suitable drift across a constant level or interval.
Abstract: We present an exact sampling method for the first passage event of a Levy process. The idea is to embed the process into another one whose first passage event can be sampled exactly, and then recover the part belonging to the former from the latter. The method is based on several distributional properties that appear to be new. We obtain general procedures to sample the first passage event of a subordinator across a regular non-increasing boundary, and that of a process with infinite Levy measure, bounded variation, and suitable drift across a constant level or interval. We give examples of application to a rather wide variety of Levy measures.

8 citations

Journal ArticleDOI
TL;DR: In this article, a model of anomalous diffusion in anisotropic medium, which is obtained as a weak limit of suitable continuous-time random walks, is presented as a possible application.

8 citations

Posted Content
TL;DR: In this article, the authors proposed an efficient method to evaluate callable and putable bonds under a wide class of interest rate models, including the popular short rate diffusion models, as well as their time changed versions with jumps.
Abstract: We propose an efficient method to evaluate callable and putable bonds under a wide class of interest rate models, including the popular short rate diffusion models, as well as their time changed versions with jumps. The method is based on the eigenfunction expansion of the pricing operator. Given the set of call and put dates, the callable and putable bond pricing function is the value function of a stochastic game with stopping times. Under some technical conditions, it is shown to have an eigenfunction expansion in eigenfunctions of the pricing operator with the expansion coefficients determined through a backward recursion. For popular short rate diffusion models, such as CIR, Vasicek, 3/2, the method is orders of magnitude faster than the alternative approaches in the literature. In contrast to the alternative approaches in the literature that have so far been limited to diffusions, the method is equally applicable to short rate jump-diffusion and pure jump models constructed from diffusion models by Bochner's subordination with a Levy subordinator.

8 citations

Journal ArticleDOI
TL;DR: In this article, an Ito multiple integral and a Stratonovich multiple integral with respect to a Levy process with finite moments up to a convenient order are presented, and a general Hu-Meyer formula that gives the relationship between both integrals is proved.
Abstract: In the framework of vector measures and the combinatorial approach to stochastic multiple integral introduced by Rota and Wallstrom [Ann. Probab. 25 (1997) 1257–1283], we present an Ito multiple integral and a Stratonovich multiple integral with respect to a Levy process with finite moments up to a convenient order. In such a framework, the Stratonovich multiple integral is an integral with respect to a product random measure whereas the Ito multiple integral corresponds to integrate with respect to a random measure that gives zero mass to the diagonal sets. A general Hu–Meyer formula that gives the relationship between both integrals is proved. As particular cases, the classical Hu–Meyer formulas for the Brownian motion and for the Poisson process are deduced. Furthermore, a pathwise interpretation for the multiple integrals with respect to a subordinator is given.

8 citations

Book ChapterDOI
01 Jan 2007
TL;DR: In this paper, the authors explore properties of subordinated d-parameter groups and show that they are semi-groups, inheriting the properties of the subordinator via a transference principle.
Abstract: In this article we explore properties of subordinated d-parameter groups We show that they are semi-groups, inheriting the properties of the subordinator via a transference principle Applications range from infinitely divisible processes on a torus to the definition of inhomogeneous d-dimensional fractional derivative operators

8 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202330
202242
202160
202056
201969
201845