Abstract
We show that for a class of Gaussian processes indexed by one dimensional time, the local times obey the behavior conjectured by Xiao.
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References
Ehm, W. (1981), Sample function properties of multiparameter stable processes. Zeit. Wahr. Theorie 56, 195–228.
Genian, D. and Horowitz, J. (1980), Occupation densities. Ann. Probab., 8, 1–67.
Genian, D., Horowitz, J. and Rosen, J. (1984), A local time analysis of intersections of Brownian paths in the plane. Ann. Probab., 12, 86–107.
Khoshenevisan, D., Xiao, Y. and Zhong, Y. (2003), Local times of additive Lévy processes. Stochastic Process. Appl., 104, no. 2, 193–216.
Mountford, T and Nualart, E (2004), Level sets of multiparameter Brownian motions. Electron. J. Probab., 9, no. 20, 594–614.
Mueller, C. and Tribe, R. (2002), Hitting properties of a random string. Electron. J. Probab., 7, 1–29.
Perkins, E. (1981), The exact Hausdorff measure of the level sets of Brownian motion. Z. Wahrsch. verw. Gebiete, 58, 373–388.
Pitt, L.D. and Tran, L.T. (1979), Local Sample Path Properties of Gaussian Fields. Ann. Probab., 7, no. 3, 477–493.
Revuz, D. and Yor, M. (1999), Continuous martingales and Brownian motion. Third edition. Springer-Verlag, New York.
Rogers, C.A. (1998), Housdorff measures. Cambridge University Press.
Samorodnitsky, G and Taqqu, M.S. (1994), Stable non-Gaussian random processes: Stochastic models with infinite variance. Stochastic Modeling. Chapman & Hall, New York.
Xiao, Y. (1997), Holder conditions for the local times and the Hausdorff measure of the level sets of Gaussian random fields. Probab. Th. Rel. Fields, 109, 129–157.
Xiao, Y. (2003), The packing measure of the trajectories of multiparameter fractional Brownian motion. Math. Proc. Camb. Phil. Soc., 135, 349–375.
Xiao, Y. (2005), Strong Local Nondeterminism and Sample Path Properties of Gaussian Random Fields. Preprint.
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Baraka, D., Mountford, T. (2008). A Law of the Iterated Logarithm for Fractional Brownian Motions. In: Donati-Martin, C., Émery, M., Rouault, A., Stricker, C. (eds) Séminaire de Probabilités XLI. Lecture Notes in Mathematics, vol 1934. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77913-1_7
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DOI: https://doi.org/10.1007/978-3-540-77913-1_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77912-4
Online ISBN: 978-3-540-77913-1
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