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A monotone operator approach to SDEs with additive noise in the Young regime.

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If you have a question about this talk, please contact Renato Velozo.

A popular approach in studying nonlinear evolution problems (a prime example being given by the evolution problem associated with the p-Laplacian) is by the use of the theory of (maximally) monotone operators. Typically in this setup, a right-hand side is required to enjoy some Lp in time regularity. We show how in the finite dimensional setting (that is in studying ODEs instead of PDEs), one can modify this approach in order to relax the regularity constraint on the right hand side to H-s for s\in (0,1/2). In particular, this relaxation can thus be interpreted as providing a pathwise theory of stochastic differential equations with an additive noise whose sample paths enjoy time regularity Hs for s\in (1/2,1), therefore providing an alternative approach to the well known Young theory for such equations.

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