Journal of Applied Mathematics and Stochastic Analysis

Volume 2006, Article ID 82838, 18 pages

http://dx.doi.org/10.1155/JAMSA/2006/82838

## Operator self-similar processes on Banach spaces

Department of Mathematics, University of Nebraska, Omaha 68182-0243, NE, USA

Received 16 March 2005; Revised 21 July 2005; Accepted 30 July 2005

Copyright © 2006 Mihaela T. Matache and Valentin Matache. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Linked References

- D. L. Armacost,
*The Structure of Locally Compact Abelian Groups*, vol. 68 of*Monographs and Textbooks in Pure and Applied Mathematics*, Marcel Dekker, New York, 1981. View at Zentralblatt MATH · View at MathSciNet - R. B. Ash,
*Real Analysis and Probability*, Academic Press, New York, 1972. View at MathSciNet - P. R. Halmos,
*A Hilbert Space Problem Book*, D. Van Nostrand, New Jersey, 1967. View at Zentralblatt MATH · View at MathSciNet - W. N. Hudson and J. D. Mason, “Operator-self-similar processes in a finite-dimensional space,”
*Transactions of the American Mathematical Society*, vol. 273, no. 1, pp. 281–297, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - Z. J. Jurek, “Limit distributions and one-parameter groups of linear operators on Banach spaces,”
*Journal of Multivariate Analysis*, vol. 13, no. 4, pp. 578–604, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - Z. J. Jurek and J. D. Mason,
*Operator-Limit Distributions in Probability Theory*, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, New York, 1993. View at Zentralblatt MATH · View at MathSciNet - S. Kantorovitz,
*Semigroups of Operators and Spectral Theory*, vol. 330 of*Pitman Research Notes in Mathematics Series*, Longman Scientific & Technical, Harlow, 1995. View at Zentralblatt MATH · View at MathSciNet - W. Krakowiak, “Operator-stable probability measures on Banach spaces,”
*Colloquium Mathematicum*, vol. 41, no. 2, pp. 313–326, 1979. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - R. G. Laha and V. K. Rohatgi, “Operator self-similar processes,”
*Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete*, vol. 50, pp. 5–25, 1979. View at Google Scholar - J. Lamperti, “Semi-stable stochastic processes,”
*Transactions of the American Mathematical Society*, vol. 104, pp. 62–78, 1962. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - V. Mandrekar and M. M. Meerschaert, “Sample moments and symmetric statistics,” in
*Stochastic Analysis on Infinite-Dimensional Spaces (Baton Rouge, La, 1994)*, vol. 310 of*Pitman Res. Notes Math. Ser.*, pp. 197–210, Longman Scientific & Technical, Harlow, 1994. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - M. M. Meerschaert and H.-P. Scheffler,
*Limit Distributions for Sums of Independent Random Vectors. Heavy Tails in Theory and Practice*, Wiley Series in Probability and Statistics: Probability and Statistics, John Wiley & Sons, New York, 2001. View at Zentralblatt MATH · View at MathSciNet - M. Moskowitz, “Homological algebra in locally compact abelian groups,”
*Transactions of the American Mathematical Society*, vol. 127, pp. 361–404, 1967. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - A. Pazy,
*Semigroups of Linear Operators and Applications to Partial Differential Equations*, vol. 44 of*Applied Mathematical Sciences*, Springer, New York, 1983. View at Zentralblatt MATH · View at MathSciNet - H. Radjavi and P. Rosenthal,
*Invariant Subspaces*, Springer, New York, 1973. View at Zentralblatt MATH · View at MathSciNet - W. Rudin,
*Functional Analysis*, McGraw-Hill, New York, 1973. View at Zentralblatt MATH · View at MathSciNet - K. Sato, “Self-similar processes with independent increments,”
*Probability Theory and Related Fields*, vol. 89, no. 3, pp. 285–300, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - G. Siegel, “Exponents of operator stable distributions in Banach spaces,” in
*Probability Theory and Mathematical Statistics, Vol. II (Vilnius, 1989)*, pp. 437–445, “Mokslas”, Vilnius, 1990. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - G. Siegel, “On the class of operator stable distributions in a separable Banach space,”
*Probability and Mathematical Statistics*, vol. 13, no. 1, pp. 33–37, 1992. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - K. Urbanik, “Lévy's probability measures on Banach spaces,”
*Studia Mathematica*, vol. 63, no. 3, pp. 283–308, 1978. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet