Parametric Estimation for Subordinators and Induced OU Processes
نویسندگان
چکیده
منابع مشابه
Subordinators, Lévy processes with no negative jumps, and branching processes
The purpose of this course is to present some simple relations connecting subordinators, Lévy processes with no negative jumps, and continuous state branching processes. To start with, we develop the main ingredients on subordinators (the LévyKhintchine formula, the Lévy-Itô decomposition, the law of the iterated logarithm, the renewal theory for the range, and the link with local times of Mark...
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For certain subordinators (Xt)t≥0 it is shown that the process (−t logXts)s>0 tends to an extremal process (η̂s)s>0 in the sense of convergence of the finite dimensional distributions. Additionally it is also shown that (z ∧ (−t logXts))s≥0 converges weakly to (z ∧ η̂s)s≥0 in D[0,∞), the space of càdlàg functions equipped with Skorohod’s J1 metric.
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Estimation methods for the Lévy density of a Lévy process are developed under mild qualitative assumptions. A classical model selection approach made up of two steps is studied. The first step consists in the selection of a good estimator, from an approximating (finite-dimensional) linear model S for the true Lévy density. The second is a data-driven selection of a linear model S, among a given...
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In this paper we introduce a large class of subordinators called special subordinators and study their potential theory. Then we study the potential theory of processes obtained by subordinating a killed symmetric stable process in a bounded open set D with special subordinators. We establish a one-to-one correspondence between the nonnegative harmonic functions of the killed symmetric stable p...
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ژورنال
عنوان ژورنال: Scandinavian Journal of Statistics
سال: 2006
ISSN: 0303-6898,1467-9469
DOI: 10.1111/j.1467-9469.2006.00498.x