Hostname: page-component-788cddb947-kc5xb Total loading time: 0 Render date: 2024-10-17T20:37:25.807Z Has data issue: false hasContentIssue false
  • English
  • Français

Differential equations in spaces of Hilbert space valued distributions

Published online by Cambridge University Press:  17 April 2009

Maxim Alshansky
Maxim Alshansky
Affiliation:
Ural State Technical University, Yekaterinburg, Russia, e-mail: mxa@mail.ur.ru
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A Gaussian measure is introduced on the space of Hilbert space valued tempered distributions. It is used to define a Hilbert space valued Q-Wiener process and a white noise process with a nuclear covariance operator Q. The proposed construction is used for solving operator-differential equations with additive noise with the operator coefficient generating an n-times integrated exponentially bounded semigroup.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 3 , December 2003 , pp. 491 - 500
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Fattorini, H.O., The Cauchy Problem (Cambridge University Press, Cambridge, 1983).Google Scholar
[2]Hida, T., Brownian motion, Applications of Mathematics 11 (Springer-Verlag, Berlin, Heidelberg, New York, 1980).CrossRefGoogle Scholar
[3]Kuo, H., Gaussian Measures in Banach Spaces, Springer Lecture Notes in Maths. 643 (Springer-Verlag, Berlin, Heidelberg, New York, 1975).CrossRefGoogle Scholar
[4]Melnikova, I. and Filinkov, A., Abstract Cauchy problems: Three approaches (Chapman & Hall, Boca Raton, 2001).CrossRefGoogle Scholar