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Some explicit Krein representations of certain subordinators, including the Gamma process
Catherine Donati-Martin,Marc Yor +1 more
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In this article, the Gamma subordinator is represented as a Krein functional of Brownian motion, using the known representations for stable subordinators and Esscher transforms, which are used to obtain Krein representations of the subordinators which govern the two parameter Poisson Dirichlet family of distributions.Abstract:
We give a representation of the Gamma subordinator as a Krein functional of Brownian motion, using the known representations for stable subordinators and Esscher transforms. In particular, we have obtained Krein representations of the subordinators which govern the two parameter Poisson-Dirichlet family of distributions.read more
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References
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Brownian Motion and Stochastic Calculus
TL;DR: In this paper, the authors present a characterization of continuous local martingales with respect to Brownian motion in terms of Markov properties, including the strong Markov property, and a generalized version of the Ito rule.
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Diffusion Processes and their Sample Paths
Kiyosi Itô,Henry P. McKean +1 more
TL;DR: In this article, the authors consider the problem of approximating the Brownian motion by a random walk with respect to the de Moivre-laplace limit theorem and show that it is NP-hard.
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The Variance Gamma Process and Option Pricing
TL;DR: In this article, a three-parameter stochastic process, termed the variance gamma process, is developed as a model for the dynamics of log stock prices, which is obtained by evaluating Brownian motion with drift at a random time given by a gamma process.
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TL;DR: In this paper, the second volume follows on from the first, concentrating on stochastic integrals, stochy differential equations, excursion theory and the general theory of processes.
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Some Explicit Krein Representations of Certain Subordinators, Including the Gamma Process
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