Every fixed area increment of an infinite-dimensional continuous martingale lies almost surely in the separable little weak trace class S^0_{1,infinity}, with sharp Gaussian examples and an anisotropic skew/symmetric response splitting.
Rough differential equation in Banach space driven by weak geometric p-rough path
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abstract
By using an explicit ordinary differential equation to approximate the exponential solution flow, we extend the universal limit theorem to rough differential equation in Banach space driven by weak geometric rough path, and give the quantitative dependence of solution in term of the initial value, vector field and driving rough path.
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math.PR 1years
2026 1verdicts
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Infinite-Dimensional Levy Area: Sharp Operator-Ideal Regularity and Anisotropic Ito Geometry
Every fixed area increment of an infinite-dimensional continuous martingale lies almost surely in the separable little weak trace class S^0_{1,infinity}, with sharp Gaussian examples and an anisotropic skew/symmetric response splitting.