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Linearization and local stability of random dynamical systems


Authors: Igor V. Evstigneev, Sergey A. Pirogov and Klaus R. Schenk-Hoppé
Journal: Proc. Amer. Math. Soc. 139 (2011), 1061-1072
MSC (2010): Primary 37H05, 34F05; Secondary 91G80, 37H15
DOI: https://doi.org/10.1090/S0002-9939-2010-10647-0
Published electronically: September 24, 2010
MathSciNet review: 2745656
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Abstract: 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
Email: igor.evstigneev@manchester.ac.uk

Sergey A. Pirogov
Affiliation: Institute for Information Transmission Problems, Academy of Sciences of Russia, GSP-4, Moscow, 101447, Russia
Email: pirogov@mail.ru

Klaus R. Schenk-Hoppé
Affiliation: School of Mathematics and Leeds University Business School, University of Leeds, Leeds LS2 9JT, United Kingdom
Email: k.r.schenk-hoppe@leeds.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-2010-10647-0
Keywords: Local stability, linearization, random fixed points, random dynamical systems, mathematical finance.
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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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