Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Path properties for $l^ \infty$-valued Gaussian processes
HTML articles powered by AMS MathViewer

by Miklós Csörgő, Zheng Yan Lin and Qi Man Shao PDF
Proc. Amer. Math. Soc. 121 (1994), 225-236 Request permission


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.
  • Endre Csáki and Miklós Csörgő, Fernique type inequalities for not necessarily Gaussian processes, C. R. Math. Rep. Acad. Sci. Canada 12 (1990), no. 5, 149–154. MR 1077478
  • Endre Csáki and Miklós Csörgő, Inequalities for increments of stochastic processes and moduli of continuity, Ann. Probab. 20 (1992), no. 2, 1031–1052. MR 1159584
  • E. Csáki, M. Csörgő, Z. Y. Lin, and P. Révész, On infinite series of independent Ornstein-Uhlenbeck processes, Stochastic Process. Appl. 39 (1991), no. 1, 25–44. MR 1135082, DOI 10.1016/0304-4149(91)90029-C
  • Endre Csáki, Miklós Csörgő, and Qi Man Shao, Fernique type inequalities and moduli of continuity for $l^2$-valued Ornstein-Uhlenbeck processes, Ann. Inst. H. Poincaré Probab. Statist. 28 (1992), no. 4, 479–517 (English, with English and French summaries). MR 1193082
  • —, Moduli of continuity for ${l^p}$-valued Gaussian processes, Tech. Rep. Ser. Lab. Res. Stat. Probab. No. 160, Carleton University-University of Ottawa.
  • Miklós Csörgő and Zheng Yan Lin, On moduli of continuity for Gaussian and $l^2$-norm squared processes generated by Ornstein-Uhlenbeck processes, Canad. J. Math. 42 (1990), no. 1, 141–158. MR 1043516, DOI 10.4153/CJM-1990-009-6
  • M. Csörgő and Q. M. Shao, Strong limit theorems for large and small increments of ${l^p}$-valued Gaussian processes, Ann. Probab. 21 (1993).
  • D. A. Dawson, Stochastic evolution equations, Math. Biosci. 15 (1972), 287–316. MR 321178, DOI 10.1016/0025-5564(72)90039-9
  • Xavier Fernique, La régularité des fonctions aléatoires d’Ornstein-Uhlenbeck à valeurs dans $l^2;$ le cas diagonal, C. R. Acad. Sci. Paris Sér. I Math. 309 (1989), no. 1, 59–62 (French, with English summary). MR 1004940
  • —, Sur la régularité de certaines fonctions aléatoires d’Ornstein-Uhlenbeck, Ann. Inst. H. Poincaré Probab. Statist. 26 (1990), 399-417.
  • I. Iscoe, M. B. Marcus, D. McDonald, M. Talagrand, and J. Zinn, Continuity of $l^2$-valued Ornstein-Uhlenbeck processes, Ann. Probab. 18 (1990), no. 1, 68–84. MR 1043937, DOI 10.1214/aop/1176990938
  • I. Iscoe and D. McDonald, Large deviations for $l^2$-valued Ornstein-Uhlenbeck processes, Ann. Probab. 17 (1989), no. 1, 58–73. MR 972771, DOI 10.1214/aop/1176991494
  • B. Schmuland, Dirichlet forms and infinite dimensional Ornstein-Uhlenbeck processes, Ph.D. Dissertation, Carleton University, Ottawa, 1987.
  • Byron Schmuland, Some regularity results on infinite-dimensional diffusions via Dirichlet forms, Stochastic Anal. Appl. 6 (1988), no. 3, 327–348. MR 949683, DOI 10.1080/07362998808809152
  • B. Schmuland, Regularity of $l^2$-valued Ornstein-Uhlenbeck processes, C. R. Math. Rep. Acad. Sci. Canada 10 (1988), no. 2, 119–124. MR 933225
  • Byron Schmuland, Moduli of continuity for some Hilbert space valued Ornstein-Uhlenbeck processes, C. R. Math. Rep. Acad. Sci. Canada 10 (1988), no. 4, 197–201. MR 955099
  • B. Schmuland, Sample path properties of $l^p$-valued Ornstein-Uhlenbeck processes, Canad. Math. Bull. 33 (1990), no. 3, 358–366. MR 1077111, DOI 10.4153/CMB-1990-060-9
Similar Articles
Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 121 (1994), 225-236
  • MSC: Primary 60G15; Secondary 60F15, 60G10, 60G17
  • DOI:
  • MathSciNet review: 1231032