Let be a subfractional Brownian motion in . We prove that is strongly locally nondeterministic.
References
[1]
Kolmogorov, A.N. (1940) Wienersche Spiralen und einige andere interessante Kurven im Hilbertschen Raum. C.R. (Doklady) Acad. Sci. URSS (N.S.), 26, 115-118.
[2]
Mandelbrot, B. and van Ness, J.W. (1968) Fractional Brownian Motions, Fractional Noises and Applications. SIAM Review, 10, 422-437. http://dx.doi.org/10.1137/1010093
[3]
Samorodnitsky, G. and Taqqu, M.S. (1994) Stable Non-Gaussian Random Processes. Stochastic Models with Infinite Variance. Stochastic Modeling. Chapman & Hall, New York.
[4]
Anh, V.V., Angulo, J.M. and Ruiz-Medina, M.D. (1999) Possible Long-Range Dependence in Fractional Random Fields. Journal of Statistical Planning and Inference, 80, 95-110. http://dx.doi.org/10.1016/S0378-3758(98)00244-4
[5]
Benassi, A., Bertrand, P., Cohen, S. and Istas, J. (2000) Identification of the Hurst Index of a Step Fractional Brownian Motion. Statistical Inference for Stochastic Processes, 3, 101-111. http://dx.doi.org/10.1023/A:1009997729317
[6]
Benson, D.A., Meerschaert, M.M. and Baeumer, B. (2006) Aquifer Operator-Scaling and the Effect on Solute Mixing and Dispersion. Water Resources Research, 42, W01415. http://dx.doi.org/10.1029/2004wr003755
[7]
Bonami, A. and Estrade, A. (2003) Anisotropic Analysis of Some Gaussian Models. Journal of Fourier Analysis and Applications, 9, 215-236. http://dx.doi.org/10.1007/s00041-003-0012-2
[8]
Cheridito, P., Kawaguchi, H. and Maejima, M. (2003) Fractional Ornstein-Uhlenbeck Processes. Electronic Journal of Probability, 8, 14 p.
[9]
Mannersalo, P. and Norros, I. (2002) A Most Probable Path Approach to Queueing Systems with General Gaussian Input. Computer Network, 40, 399-412. http://dx.doi.org/10.1016/S1389-1286(02)00302-X
[10]
Tudor, C.A. and Xiao, Y. (2007) Sample Path Properties of Bifractional Brownian Motion. Bernoulli, 13, 1023-1052.
http://dx.doi.org/10.3150/07-BEJ6110
[11]
Lamperti, J. (1962) Semi-Stable Stochastic Processes. Transactions of the American Mathematical Society, 104, 62-78.
http://dx.doi.org/10.1090/S0002-9947-1962-0138128-7
[12]
Xiao, Y. (2007) Strong Local Non-Determinism of Gaussian Random Fields and Its Applications. In: Lai, T.-L., Shao, Q.-M. and Qian, L., Eds., Asymptotic Theory in Probability and Statistics with Applications, Higher Education Press, Beijing, 136-176.
[13]
Bojdecki, T., Gorostiza, L.G. and Talarczyk, A. (2004) Sub-Fractional Brownian Motion and Its Relation to Occupation Times. Statistics and Probability Letters, 69, 405-419. http://dx.doi.org/10.1016/j.spl.2004.06.035
[14]
Dzhaparidze, K. and Van Zanten, H. (2004) A Series Expansion of Fractional Brownian Motion. Probability Theory and Related Fields, 103, 39-55. http://dx.doi.org/10.1007/s00440-003-0310-2
[15]
Tudor, C. (2007) Some Properties of the Sub-Fractional Brownian Motion. Stochastics, 79, 431-448.
http://dx.doi.org/10.1080/17442500601100331
[16]
Pitman, E.J.G. (1968) On the Behavior of the Characteristic Function of a Probability Distribution in the Neighborhood of the Origin. Journal of the Australian Mathematical Society, 8 423-443.
http://dx.doi.org/10.1017/S1446788700006121
[17]
Cuzick, J. and Du Preez, J.P. (1982) Joint Continuity of Gaussian Local Times. Annals of Probability, 10, 810-817.
http://dx.doi.org/10.1214/aop/1176993789
![\"\"](\"Edit_2b2ffe61-b3b6-4116-bc26-359e2111d69e.bmp\")
be a subfractional Brownian motion in ![\"\"](\"Edit_8481912e-a238-45f2-9147-e8856af3da7d.bmp\")
. We prove that ![\"\"](\"Edit_2afa3cff-2ea2-4a5f-8472-39453df46b87.bmp\")
is strongly locally nondeterministic.
