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math.PR2024
Multidimensional specific relative entropy between continuous martingales
Julio Backhoff, Edoardo Kimani Bellotto
In continuous time, the laws of martingales tend to be singular to each other. Notably, N. Gantert introduced the concept of specific relative entropy between real-valued continuou…
math.PR2024
Geometric Martingale Benamou-Brenier transport and geometric Bass martingales
Julio Backhoff, Gregoire Loeper, Jan Obloj
We introduce and study geometric Bass martingales. Bass martingales were introduced in \cite{Ba83} and studied recently in a series of works, including \cite{BaBeHuKa20,BaBeScTs23}…