One-dimensional game-theoretic differential equations
Abstract
We provide a very brief introduction to typical paths and the corresponding It\o type integration. Relying on this robust It\o integration, we prove an existence and uniqueness result for one-dimensional differential equations driven by typical paths with non-Lipschitz continuous coefficients in the spirit of Yamada--Watanabe as well as an approximation result in the spirit of Doss--Sussmann.
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