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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.

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Linearization and local stability of random dynamical systems
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by Igor V. Evstigneev, Sergey A. Pirogov and Klaus R. Schenk-Hoppé PDF
Proc. Amer. Math. Soc. 139 (2011), 1061-1072 Request permission


The paper examines questions of local asymptotic stability of random dynamical systems. Results concerning stochastic dynamics in general metric spaces, as well as in Banach spaces, are obtained. The results pertaining to Banach spaces are based on the linearization of the systems under study. The general theory is motivated (and illustrated in this paper) by applications in mathematical finance.
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Additional Information
  • Igor V. Evstigneev
  • Affiliation: Department of Economics, University of Manchester, Manchester M13 9PL, United Kingdom
  • MR Author ID: 210292
  • Email:
  • Sergey A. Pirogov
  • Affiliation: Institute for Information Transmission Problems, Academy of Sciences of Russia, GSP-4, Moscow, 101447, Russia
  • MR Author ID: 231708
  • Email:
  • Klaus R. Schenk-Hoppé
  • Affiliation: School of Mathematics and Leeds University Business School, University of Leeds, Leeds LS2 9JT, United Kingdom
  • Email:
  • Received by editor(s): March 29, 2010
  • Published electronically: September 24, 2010
  • Additional Notes: The authors gratefully acknowledge financial support from the Swiss National Center of Competence in Research “Financial Valuation and Risk Management” (project “Behavioural and Evolutionary Finance”) and from the Finance Market Fund, Norway (projects “Stochastic Dynamics of Financial Markets” and “Stability of Financial Markets: An Evolutionary Approach”).
  • Communicated by: Yingfei Yi
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 1061-1072
  • MSC (2010): Primary 37H05, 34F05; Secondary 91G80, 37H15
  • DOI:
  • MathSciNet review: 2745656