A random fixed point theorem and the random graph transformation

DOI10.1006/jmaa.1998.6008zbMath0931.37019OpenAlexW2061935186MaRDI QIDQ1270923

Björn Schmalfuss

Publication date: 3 November 1998

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.1998.6008

zbMATH Keywords

random dynamical systemsstationary solutionsunstable manifoldrandom fixed point theoremgraph transformationsemicoupled random differential equation

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) Generation, random and stochastic difference and differential equations (37H10) General theory of random and stochastic dynamical systems (37H05)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A stochastic version of center manifold theory
• Convex analysis and measurable multifunctions
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• Random fixed point theorems for multivalued mappings
• Some Random Fixed Point Theorems for Condensing and Nonexpansive Operators
• Random Fixed Point Theorems for Measurable Multifunctions in Banach Spaces
• Random Approximations and Random Fixed Point Theorems for Non-Self-Maps
• Fixed point theorems in probabilistic analysis
• Invariant Manifolds for Infinite Dimensional Random Dynamical Systems
• On the Nature of the Spectrum of Singular Second Order Linear Differential Equations
• Invariant manifolds

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