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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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.

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Stabilization of evolution equations by noise
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by Anna A. Kwiecińska PDF
Proc. Amer. Math. Soc. 130 (2002), 3067-3074 Request permission

Abstract:

We consider a deterministic equation of evolution \[ X’(t)=AX(t)dt,\] in a separable, real Hilbert space. We prove that if $A$ generates a $C_0$-semigroup, then this equation can be stabilized, in terms of Lyapunov exponents, by noise.
References
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Additional Information
  • Anna A. Kwiecińska
  • Affiliation: Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-950 Warszawa, Poland
  • Email: akwiecin@impan.gov.pl
  • Received by editor(s): April 2, 2001
  • Received by editor(s) in revised form: June 1, 2001
  • Published electronically: March 29, 2002
  • Additional Notes: This research was partially supported by KBN grant 2 P03A 016 16
  • Communicated by: Claudia M. Neuhauser
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 130 (2002), 3067-3074
  • MSC (2000): Primary 35K90, 37L55; Secondary 47D06
  • DOI: https://doi.org/10.1090/S0002-9939-02-06443-2
  • MathSciNet review: 1908931