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2-d signature of images and texture classification
We introduce a proper notion of 2-dimensional signature for images.
Skorohod and Stratonovich integrals for controlled processes
Given a continuous Gaussian process $x$ which gives rise to a $p$-geometric rough path for $p\in (2, 3)$, and a general continuous process $y$ controlled by $x$, under proper conditions we establish the relationship between the Skorohod integral $\int_0^t y_s {\mathrm{d}}^\diamond x_s$ and the Stratonovich integral $\int_0^t y_s {\mathrm{d}} {\mathbf x}_s$.
Probability
Augmented Gaussian Random Field: Theory and Computation
We prove that under certain conditions, the observable and its derivatives of any order are governed by a single Gaussian random field, which is the aforementioned AGRF.
Statistics Theory Probability Statistics Theory
