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
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.References
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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: igor.evstigneev@manchester.ac.uk
- Sergey A. Pirogov
- Affiliation: Institute for Information Transmission Problems, Academy of Sciences of Russia, GSP-4, Moscow, 101447, Russia
- MR Author ID: 231708
- 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
- 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: https://doi.org/10.1090/S0002-9939-2010-10647-0
- MathSciNet review: 2745656