Fractional Brownian sheets run with nonlinear clocks

Journal of Mathematical Physics

Volumn 53, Issue 1, 2012, Pages

  Wu, Dongsheng ^a  

^a University of Alabama in Huntsville ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84856446644     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3677983     Document Type: Article

References (23)

1. Adler R.J. The Geometry of Random Fields 1981, (Wiley, New York)
2. Ayache A. Wu D. Xiao Y. Joint continuity of the local times of fractional Brownian sheets. Ann. I.H.P. Probab. Stat. 2008, 44:727. 10.1214/07-AIHP131.
3. Ayache A. Xiao Y. Asymptotic growth properties and Hausdorff dimension of fractional Brownian sheets. J. Fourier Anal. Appl. 2005, 11:407. 10.1007/s00041-005-4048-3.
4. Cushman J. O'Malley D. Park M. Anomalous diffusion as modeled by a nonstationary extension of Brownian motion. Phys. Rev. E 2009, 79:032101. 10.1103/PhysRevE.79.032101.
5. Dunker T. Estimates for the small ball probabilities of the fractional Brownian sheet. J. Theor. Probab. 2000, 13:357. 10.1023/A:1007897525164.
6. Ehm W. Sample function properties of multi-parameter stable processes. Z. Wahrscheinlichkeitstheor. Verwandte Geb. 1981, 56:195. 10.1007/BF00535741.
7. Falconer K.J. Fractal Geometry: Mathematical Foundations And Applications 1990, (Wiley, Chichester)
8. Geman D. Horowitz J. Occupation densities. Ann. Probab. 1980, 8:1. 10.1214/aop/1176994824.
9. Geman D. Horowitz J. Rosen J. A local time analysis of intersections of Brownian paths in the plane. Ann. Probab. 1984, 12:86. 10.1214/aop/1176993375.
10. Kamont A. On the fractional anisotropic Wiener field. Probab. Math. Statist. 1996, 16:85.
11. Khoshnevisan D. Multiparameter Processes: An Introduction to Random Fields 2002, (Springer, New York)
12. Mandelbrot B. Van Ness J. Fractional Brownian motion, fractional noises and applications. SIAM Rev. 1968, 10:422. 10.1137/1010093.
13. Mason D.M. Shi Z. Small deviations for some multi-parameter Gaussian processes. J. Theor. Probab. 2001, 14:213. 10.1023/A:1007833401562.
14. Nualart D. Ortiz-Latorre S. Intersection local time for two independent fractional Brownian motions. J. Theor. Probab. 2007, 20:759. 10.1007/s10959-007-0106-x.
15. Øksendal B. Zhang T. Multiparameter fractional Brownian motion and quasi-linear stochastic partial differential equations. Stoch. Stoch. Rep. 2001, 71:141.
16. O'Malley D. Cushman J. Fractional Brownian motion run with a nonlinear clock. Phys. Rev. E 2010, 82:032102. 10.1103/PhysRevE.82.032102.
17. Park M. Cushman J. The complexity of Brownian processes run with nonlinear clocks. Mod. Phys. Lett. 2011, 25:1. 10.1142/S0217984911025481.
18. Wolpert R. Wiener path intersections and local time. J. Funct. Anal. 1978, 30:329. 10.1016/0022-1236(78)90061-7.
19. Wu D. Xiao Y. Geometric properties of fractional Brownian sheets. J. Fourier Anal. Appl. 2007, 13:1. 10.1007/s00041-005-5078-y.
20. Wu D. Xiao Y. Regularity of intersection local times of fractional Brownian motions. J. Theor. Probab. 2010, 23:972. 10.1007/s10959-009-0221-y.
21. Xiao Y. Hölder conditions for the local times and the Hausdorff measure of the level sets of Gaussian random fields. Probab. Theory Relat. Fields 1997, 109:129. 10.1007/s004400050128.
22. Xiao Y. Sample path properties of anisotropic Gaussian random fields. A Minicourse on Stochastic Partial Differential Equations 2009, 145-212. D.Khoshnevisan, F.Rassoul-Aghain edited by and (Springer, New York
23. Xiao Y. Zhang T. Local times of fractional Brownian sheets. Probab. Theory Relat. Fields 2002, 124:204. 10.1007/s004400200210.