From the 1 of 7 linked papers with an AI index.
4 papers · 1 filter
Higher-order variation and pathwise Ito calculus on manifolds
Rama Cont
We develop an intrinsic calculus for smooth functions of paths of arbitrarily low regularity on smooth manifolds and define pathwise integrals for exact differential forms along su…
A pathwise Ito formula for weakly differentiable functions
Anna Ananova, Rama Cont
We prove a version of Föllmer's pathwise Itô formula for weakly differentiable functions of continuous paths with finite quadratic variation along a sequence of partitions. For eac…
Mimicking diffusion processes with differential equations
Rama Cont
The probability-flow ordinary differential equation (PF-ODE) associated with a diffusion process is widely used in score-based generative modeling as a deterministic sampler that r…
Causal transport on path space
Rama Cont, Fang Rui Lim
We study properties of causal couplings for probability measures on the space of continuous functions. We first provide a characterization of bicausal couplings between weak soluti…