منابع مشابه
Basics of Lévy Processes *
This is a draft Chapter from a book by the authors on “Lévy Driven Volatility Models”.
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Using the Wiener–Hopf factorization, it is shown that it is possible to bound the path of an arbitrary Lévy process above and below by the paths of two random walks. These walks have the same step distribution, but different random starting points. In principle, this allows one to deduce Lévy process versions of many known results about the large-time behavior of random walks. This is illustrat...
متن کاملLévy processes in free probability.
This is the continuation of a previous article that studied the relationship between the classes of infinitely divisible probability measures in classical and free probability, respectively, via the Bercovici-Pata bijection. Drawing on the results of the preceding article, the present paper outlines recent developments in the theory of Lévy processes in free probability.
متن کاملSkewness Premium with Lévy Processes ∗
We study the skewness premium (SK) introduced by Bates (1991) in a general context using Lévy Processes. Under a symmetry condition Fajardo and Mordecki (2006) obtain that SK is given by the Bate’s x% rule. In this paper we study SK under the absence of that symmetry condition. More exactly, we derive sufficient conditions for SK to be positive, in terms of the characteristic triplet of the Lév...
متن کاملDynamical approach to Lévy processes.
We derive the diffusion process generated by a correlated dichotomous fluctuating variable y starting from a Liouville-like equation by means of a projection procedure. This approach makes it possible to derive all statistical properties of the diffusion process from the correlation function of the dichotomous fluctuating variable Fy(t). Of special interest is that the distribution of the times...
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ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2018
ISSN: 1050-5164
DOI: 10.1214/17-aap1306