Stochastic invariance of closed sets with non-Lipschitz coefficients

21 Jun 2018  ·  Jaber Eduardo Abi CEREMADE, Bouchard Bruno CEREMADE, Illand Camille, Jaber Eduardo ·

This paper provides a new characterization of the stochastic invariance of a closed subset of R^d with respect to a diffusion. We extend the well-known inward pointing Stratonovich drift condition to the case where the diffusion matrix can fail to be differentiable: we only assume that the covariance matrix is... In particular, our result can be directly applied to construct affine diffusions and polynomial preserving diffusions on any arbitrary closed set. read more

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Probability