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math.PR2025
A geometric model of synthetic filtrations via context-dependent time
Takanori Adachi
Classical filtrations in probability theory formalize the accumulation of information along a linear time axis: the past is unique and the present evolves into an uncertain future.…
math.PR2016★ 2 cited
A Category of Probability Spaces
Takanori Adachi, Yoshihiro Ryu
We introduce a category Prob of probability spaces whose objects are all probability spaces and arrows are corresponding to measurable functions satisfying an absolutely continuous…