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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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Book ChapterDOI
01 Jan 1997
TL;DR: For a large class of random times T the distribution of relative lengths prior to T is the same as if T were a fixed time as discussed by the authors, and absolute continuity relations are obtained which relate the law of the relative lengths at time T to the law at fixed time.
Abstract: Results are obtained concerning the distribution of ranked relative lengths of excursions of a recurrent Markov process from a point in its state space whose inverse local time process is a stable subordinator. It is shown that for a large class of random times T the distribution of relative excursion lengths prior to T is the same as if T were a fixed time. It follows that the generalized arc-sine laws of Lamperti extend to such random times T. For some other random times T, absolute continuity relations are obtained which relate the law of the relative lengths at time T to the law at a fixed time.

29 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that the two-time correlation function that allows one to establish aging converges almost surely to the arcsine law distribution function, as predicted in the physics literature, in the optimal domain of the time-scale and temperature parameters where this result can be expected to hold.
Abstract: We consider Metropolis dynamics of the Random Energy Model. We prove that the classical two-time correlation function that allows one to establish aging converges almost surely to the arcsine law distribution function, as predicted in the physics literature, in the optimal domain of the time-scale and temperature parameters where this result can be expected to hold. To do this we link the two-time correlation function to a certain continuous-time clock process which, after proper rescaling, is proven to converge to a stable subordinator almost surely in the random environment and in the fine $$J_1$$ -topology of Skorohod. This fine topology then enables us to deduce from the arcsine law for stable subordinators the asymptotic behavior of the two-time correlation function that characterizes aging.

29 citations

Journal ArticleDOI
TL;DR: In this paper, the authors studied the fractional Poisson process (FPP) time-changed by an independent Levy subordinator and the inverse of the Levy subordinators, which they call TCFPP-I and TC FPP-II, respectively.
Abstract: In this paper, we study the fractional Poisson process (FPP) time-changed by an independent Levy subordinator and the inverse of the Levy subordinator, which we call TCFPP-I and TCFPP-II, respectively. Various distributional properties of these processes are established. We show that, under certain conditions, the TCFPP-I has the long-range dependence property, and also its law of iterated logarithm is proved. It is shown that the TCFPP-II is a renewal process and its waiting time distribution is identified. The bivariate distributions of the TCFPP-II are derived. Some specific examples for both the processes are discussed. Finally, we present simulations of the sample paths of these processes.

28 citations

Journal ArticleDOI
TL;DR: The Hausdorff dimension of the range of an arbitrary subordinator is exactly determined in terms of the rate of linear drift and the Levy measure of the subordinator.
Abstract: The Hausdorff dimension of the range of an arbitrary subordinator is exactly determined in terms of the rate of linear drift and the Levy measure of the subordinator. This generalizes the result of Blumenthal and Getoor: that for a stable subordinator of indexσ, the dimension of the range isσ.

28 citations

Journal ArticleDOI
TL;DR: In this paper, the authors provided a systematic study on effectively approximating the Gerber-Shiu functions, which is a hardly touched topic in the current literature, by incorporating the recently popular Fourier-cosine method.
Abstract: In this article, we provide a systematic study on effectively approximating the Gerber–Shiu functions, which is a hardly touched topic in the current literature, by incorporating the recently popular Fourier-cosine method. Fourier-cosine method has been a prevailing numerical method in option pricing theory since the work of Fang and Oosterlee (2009). Our approximant of Gerber–Shiu functions under Levy subordinator model has O ( n ) computational complexity in comparison with that of O ( n log n ) via the fast Fourier transform algorithm. Also, for Gerber–Shiu functions within our proposed refined Sobolev space, we introduce an explicit error bound, which seems to be absent from the literature. In contrast with our previous work (Chau et al., 2015), this error bound is more conservative without making heavy assumptions on the Fourier transform of the Gerber–Shiu function. The effectiveness of our result will be further demonstrated in the numerical studies.

27 citations


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