منابع مشابه
Stochastic Bounds for Lévy Processes
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...
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We develop a notion of nonlinear stochastic integrals for hyperfinite Lévy processes, and use it to find exact formulas for expressions which are intuitively of the form Pt s=0 φ(ω, dls, s) and Qt s=0 ψ(ω, dls, s), where l is a Lévy process. These formulas are then applied to geometric Lévy processes, infinitesimal transformations of hyperfinite Lévy processes, and to minimal martingale measure...
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Lévy processes refer to a class of stochastic processes, for example, Poisson processes and Brownian motions, and play an important role in stochastic processes and machine learning. Therefore, it is essential to study risk bounds of the learning process for time-dependent samples drawn from a Lévy process (or briefly called learning process for Lévy process). It is noteworthy that samples in t...
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In this paper we generalize the martingale of Kella and Whitt to the setting of Lévy-type processes and show that under some quite minimal conditions the local martingales are actually L martingales which upon dividing by the time index converge to zero a.s. and in L. We apply these results to generalize known decomposition results for Lévy queues with secondary jump inputs and queues with serv...
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This is a draft Chapter from a book by the authors on “Lévy Driven Volatility Models”.
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2004
ISSN: 0091-1798
DOI: 10.1214/009117904000000315