653 citations · 2.9k across the 53 of their papers we have counts for
57 papers
Measuring the roughness of a signal
Rama Cont, Purba Das
We study the non-parametric estimation of the roughness of a path from discretely sampled observations. Our approach is based on the concept of normalized power variation of a path…
Probability flow ODEs in score-based and reflected diffusion models
Rama CONT
Probability-flow ordinary differential equations (PF-ODEs) are widely used as deterministic samplers for score-based diffusion models. Their usual justification is that the Fokker-…
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. The regularity of paths is defined in terms of a -th variation…
Functional representation and functional calculus for controlled paths
Anna Ananova, Rama Cont
We study the relation between non-anticipative functional calculus and compatible families of controlled paths. For a non-anticipative functional satisfying horizontal Lipschitz re…
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…