A Peano-Like Theorem for Stochastic Differential Equations with Nonlocal Sample Dependence

DOI10.1080/07362994.2012.727142zbMath1273.60081OpenAlexW2165986302MaRDI QIDQ4916398

Thomas Lorenz, Peter E. Kloeden

Publication date: 22 April 2013

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

Full work available at URL: https://doi.org/10.1080/07362994.2012.727142

zbMATH Keywords

existence and uniqueness theoremsstrong solutionsmean-fieldnonlocal dependenceItô stochastic differential equationsMcKean-Vlasov

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Random operators and equations (aspects of stochastic analysis) (60H25) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35)

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Differential equations for closed sets in a Banach space, survey and extension ⋮ A viability theorem for set-valued states in a Hilbert space ⋮ Mean-square random dynamical systems ⋮ Nonlocal multi-scale traffic flow models: analysis beyond vector spaces ⋮ Some Classes of Stochastic Differential Equations as an Alternative Modeling Approach to Biomedical Problems ⋮ Perturbed nonlocal stochastic functional differential equations

Cites Work

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• Existence results and the moment estimate for nonlocal stochastic differential equations with time-varying delay
• Mutational analysis. A joint framework for Cauchy problems in and beyond vector spaces
• Stochastic Differential Equations with Nonlocal Sample Dependence
• Functional Analysis
• A CLASS OF MARKOV PROCESSES ASSOCIATED WITH NONLINEAR PARABOLIC EQUATIONS
• Stochastic differential equations. An introduction with applications.

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