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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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Journal ArticleDOI
Jun Cai1
TL;DR: In this paper, a compound Poisson surplus process is invested in a stochastic interest process which is assumed to be a Levy process, and recursive and integral equations for ruin probabilities with such an investment are derived.

75 citations

Journal ArticleDOI
TL;DR: In this article, the authors developed a new advection-dispersion equation with an additional fractional time derivative of order between 1 and 2, which is related to the probability distribution of particle waiting times and the subordinator is given as the first passage time density of the waiting time process.
Abstract: Previous work showed how moving particles that rest along their trajectory lead to time-nonlocal advection–dispersion equations. If the waiting times have infinite mean, the model equation contains a fractional time derivative of order between 0 and 1. In this article, we develop a new advection–dispersion equation with an additional fractional time derivative of order between 1 and 2. Solutions to the equation are obtained by subordination. The form of the time derivative is related to the probability distribution of particle waiting times and the subordinator is given as the first passage time density of the waiting time process which is computed explicitly.

74 citations

Journal ArticleDOI
TL;DR: In this article, a large class of subordinate Brownian motions without diffusion component and with φ comparable to a regularly varying function at infinity were considered, and sharp two-sided estimates on the Green functions of these motions were obtained in any bounded κ-fat open set D. If D is a bounded C 1,1 open set, the boundary Harnack principle was established in terms of the distance to the boundary.
Abstract: A subordinate Brownian motion is a Levy process that can be obtained by replacing the time of the Brownian motion by an independent subordinator. The infinitesimal generator of a subordinate Brownian motion is �φ(�Δ), where φ is the Laplace exponent of the subordinator. In this paper, we consider a large class of subordinate Brownian motions without diffusion component and with φ comparable to a regularly varying function at infinity. This class of processes includes symmetric stable processes, relativistic stable processes, sums of independent symmetric stable processes, sums of independent relativistic stable processes and much more. We give sharp two-sided estimates on the Green functions of these subordinate Brownian motions in any bounded κ-fat open set D.W henD is a bounded C 1,1 open set, we establish an explicit form of the estimates in terms of the distance to the boundary. As a consequence of such sharp Green function estimates, we obtain a boundary Harnack principle in C 1,1 open sets with explicit rate of decay.

73 citations

Journal ArticleDOI
01 Oct 2015
TL;DR: In this article, the authors studied the asymptotic behavior of the time-changed stochas-tic process f X(t) = B( f S(t)), where B is a standard one-dimensional Brow-nian motion and f S is the (generalized) inverse of a subordinator.
Abstract: We study the asymptotic behaviour of the time-changed stochas- tic process f X(t) = B( f S(t)), where B is a standard one-dimensional Brow- nian motion and f S is the (generalized) inverse of a subordinator, i.e. the first-passage time process corresponding to an increasing Lprocess with Laplace exponent f. This type of processes plays an important role in statis- tical physics in the modeling of anomalous subdiffusive dynamics. The main result of the paper is the proof of the mixing property for the sequence of stationary increments of a subdiffusion process. We also investigate various martingale properties, derive a generalized Feynman-Kac formula, the laws of large numbers and of the iterated logarithm for f X.

72 citations

Journal ArticleDOI
TL;DR: In this article, the authors derived the joint density of the lengths of the n longest excursions away from 0 up to a fixed time for the Poisson-Dirichlet process.

70 citations


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