Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Path properties for $ l\sp \infty$-valued Gaussian processes


Authors: Miklós Csörgő, Zheng Yan Lin and Qi Man Shao
Journal: Proc. Amer. Math. Soc. 121 (1994), 225-236
MSC: Primary 60G15; Secondary 60F15, 60G10, 60G17
DOI: https://doi.org/10.1090/S0002-9939-1994-1231032-9
MathSciNet review: 1231032
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove moduli of continuity results for $ {l^\infty }$-valued Gaussian processes in general, as well as for $ {l^\infty }$-valued Ornstein-Uhlenbeck processes in particular.


References [Enhancements On Off] (What's this?)

  • [1] E. Csáki, and M. Csörgő, Fernique type inequalities for not necessarily Gaussian processes, C. R. Math. Rep. Acad. Sci. Canada 12 (1990), 149-154. MR 1077478 (91j:60072)
  • [2] -, Inequalities for increments of stochastic processes and moduli of continuity, Ann. Probab. 20 (1992), 1031-1052. MR 1159584 (93c:60055)
  • [3] E. Csáki, M. Csörgő, Z. Y. Lin, and P. Révész, On infinite series of independent Ornstein-Uhlenbeck processes, Stochastic Process. Appl. 39 (1991), 25-44. MR 1135082 (93a:60058)
  • [4] E. Csáki, M. Csörgő, and Q. M. Shao, Fernique type inequalities and moduli of continuity for $ {l^2}$-valued Ornstein-Uhlenbeck processes, Ann. Inst. H. Poincaré Probab. Statist. 28 (1992), 479-517. MR 1193082 (93k:60095)
  • [5] -, Moduli of continuity for $ {l^p}$-valued Gaussian processes, Tech. Rep. Ser. Lab. Res. Stat. Probab. No. 160, Carleton University-University of Ottawa.
  • [6] M. Csörgő and Z. Y. Lin, On moduli of continuity for Gaussian and $ {l^2}$-norm squared processes generated by Ornstein-Uhlenbeck processes, Canad. J. Math. 42 (1990), 141-158. MR 1043516 (91j:60073)
  • [7] M. Csörgő and Q. M. Shao, Strong limit theorems for large and small increments of $ {l^p}$-valued Gaussian processes, Ann. Probab. 21 (1993).
  • [8] D. A. Dawson, Stochastic evolution equations, Math. Biosciences 15 (1972), 287-316. MR 0321178 (47:9711)
  • [9] X. Fernique, La régularité des fonctions aléatoires d'Ornstein-Uhlenbeck á valeurs dans $ {l^2}$; le cas diagonal, C. R. Acad. Sci. Paris Sér I. Math. 309 (1989), 59-62. MR 1004940 (90f:60089)
  • [10] -, Sur la régularité de certaines fonctions aléatoires d'Ornstein-Uhlenbeck, Ann. Inst. H. Poincaré Probab. Statist. 26 (1990), 399-417.
  • [11] I. Iscoe, M. Marcus, D. McDonald, M. Talagrand, and J. Zinn, Continuity of $ {l^2}$-valued Ornstein-Uhlenbeck processes, Ann. Probab. 18 (1990), 68-91. MR 1043937 (91h:60064)
  • [12] I. Iscoe, and D. McDonald, Large deviations for $ {l^2}$-valued Ornstein-Uhlenbeck processes, Ann. Probab. 17 (1989), 58-73. MR 972771 (89m:60136)
  • [13] B. Schmuland, Dirichlet forms and infinite dimensional Ornstein-Uhlenbeck processes, Ph.D. Dissertation, Carleton University, Ottawa, 1987.
  • [14] -, Some regularity results on infinite dimensional diffusions via Dirichlet forms, Stochastic Anal. Appl. 6 (1988), 327-348. MR 949683 (90a:60139)
  • [15] -, Regularity of $ {l^2}$-valued Ornstein-Uhlenbeck processes, C. R. Math. Rep. Acad. Sci. Canada 10 (1988), 119-124. MR 933225 (89a:60117)
  • [16] -, Moduli of continuity for some Hilbert space valued Ornstein-Uhlenbeck processes, C. R. Math. Rep. Acad. Sci. Canada 10 (1988), 197-202. MR 955099 (90a:60081)
  • [17] -, Sample path properties of $ {l^p}$-valued Ornstein-Uhlenbeck processes, Canad. Math. Bull. 33 (1990), 358-366. MR 1077111 (92d:60050)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60G15, 60F15, 60G10, 60G17

Retrieve articles in all journals with MSC: 60G15, 60F15, 60G10, 60G17


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1231032-9
Keywords: $ {l^\infty }$-valued Gaussian processes, $ {l^\infty }$-valued Ornstein-Uhlenbeck processes, moduli of continuity, quasi-increasing functions
Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society