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)

 
 

 

Local maxima of the sample functions of the two-parameter Wiener process


Author: Lanh Tat Tran
Journal: Proc. Amer. Math. Soc. 58 (1976), 250-254
MSC: Primary 60G15; Secondary 60J65
DOI: https://doi.org/10.1090/S0002-9939-1976-0420811-2
MathSciNet review: 0420811
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that for almost all sample functions of the twoparameter Wiener process, the set of local maxima is dense in $ R_ + ^2$.


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

  • [1] N. N. Čencov (1956), Wiener random fields depending on several parameters, Dokl. Akad. Nauk SSSR 106, 607-609. (Russian) MR 17, 1101. MR 0077824 (17:1101a)
  • [2] J. Delporte (1966), Fonctions aléatoires de deux variables presque surement à échantillons continus sur un domaine rectangulaire borné, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 6, 181-205. MR 35 #3723. MR 0212858 (35:3723)
  • [3] D. Freedman (1971), Brownian motion and diffusion, Holden-Day, San Francisco, Calif. MR 45 #6074. MR 0297016 (45:6074)
  • [4] T. Kitagawa (1951), Analysis of variance applied to function spaces, Mem. Fac. Sci. Kyushu Univ. Ser. A. 6, 41-53. MR 13, 855. MR 0047299 (13:855b)
  • [5] S. Orey and W. E. Pruitt (1973), Sample functions of the $ N$-parameter Wiener process, Ann. Probability 1, no. 1, 138-163. MR 49 # 11646. MR 0346925 (49:11646)
  • [6] C. Park (1969), A generalized Paley-Wiener-Zygmund integral and its applications, Proc. Amer. Math. Soc. 23, 388-400. MR 39 #7058. MR 0245752 (39:7058)
  • [7] W. J. Park (1970), A multi-parameter Gaussian process, Ann. Math. Statist. 41, 1582-1595. MR 42 #6925. MR 0272044 (42:6925)
  • [8] J. Yeh (1960), Wiener measure in a space of functions of two variables, Trans. Amer. Math. Soc. 95, 433-450. MR 23 #A2735. MR 0125433 (23:A2735)
  • [9] -(1963a), Cameron-Martin translation theorems in the Wiener space of functions of two variables, Trans. Amer. Math. Soc. 107, 409-420. MR 32 #6565. MR 0189138 (32:6565)
  • [10] -(1963b), Orthogonal developments of functionals and related theorems in the Wiener space of functions of two variables, Pacific J. Math. 13, 1427-1436. MR 28 #2433. MR 0159216 (28:2433)
  • [11] G. Zimmerman (1972), Some sample function properties of the two-parameter Gaussian process, Ann. Math. Statist. 43, 1235-1246. MR 47 #5948. MR 0317401 (47:5948)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60G15, 60J65

Retrieve articles in all journals with MSC: 60G15, 60J65


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0420811-2
Keywords: Wiener process, local maxima, independent increments
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society