Alisa Kirichenko, Ya. Nikitin (2014)
Open Mathematics
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We find precise small deviation asymptotics with respect to the Hilbert norm for some special Gaussian processes connected to two regression schemes studied by MacNeill and his coauthors. In addition, we also obtain precise small deviation asymptotics for the detrended Brownian motion and detrended Slepian process.
Petr Lachout (2004)
Acta Universitatis Carolinae. Mathematica et Physica
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Peccati, Giovanni (2007)
Electronic Communications in Probability [electronic only]
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Petr Lachout (2001)
Kybernetika
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The paper presents a discussion on linear transformations of a Wiener process. The considered processes are collections of stochastic integrals of non-random functions w.r.t. Wiener process. We are interested in conditions under which the transformed process is a Wiener process, a Brownian bridge or an Ornstein –Uhlenbeck process.
Taniguchi, Setsuo (2006)
Electronic Communications in Probability [electronic only]
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Matsumoto, Hiroyuki, Yor, Marc (2005)
Probability Surveys [electronic only]
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Zambotti, Lorenzo (2008)
Electronic Journal of Probability [electronic only]
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Sure Mataramvura, Bernt Øksendal, Frank Proske (2004)
Annales de l'I.H.P. Probabilités et statistiques
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End Iglói, György Terdik (2003)
ESAIM: Probability and Statistics
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In this paper a new multifractal stochastic process called Limit of the Integrated Superposition of Diffusion processes with Linear differencial Generator (LISDLG) is presented which realistically characterizes the network traffic multifractality. Several properties of the LISDLG model are presented including long range dependence, cumulants, logarithm of the characteristic function, dilative stability, spectrum and bispectrum. The model captures higher-order statistics by the cumulants....