Stochastic integration by parts and functional itô calculus by Bally, V, Caramellino, L, Cont, R

“…Rama Cont's notes provide an introduction to the Functional Itô Calculus, a non-anticipative functional calculus that extends the classical Itô calculus to path-dependent functionals of stochastic processes. …”

The Ito calculus: a vector-integral approach by Ling, PD

“…The Itô calculus is the theory of stochastic integrals ∫^t₀ X_u dS_u, where S is a semimartingale, and X is a suitable previsible process. …”

Rough analysis and stochastic partial differential equations by Jin, R

“…Rama Cont,we extend the Itô calculus to paths with finite <em>p</em>-variation, where <em>p</em> is any positive real number. …”

Causal functional calculus by Henry Chiu, Rama Cont

“…For paths that possess finite quadratic variation, our approach extends the Föllmer–Ito calculus and removes previous restriction on the time partition sequence. …”

A transfer principle for branched rough paths by Ferrucci, E

“…These results extend previous work on 3 > p-rough paths [ABCF22], itself a generalisation of the Itô calculus on manifolds developed by Schwartz, Meyer and Émery [Sch82, Mey81, É89, É90], to the setting of non-geometric rough calculus of arbitrarily low regularity…”

Roughness properties of paths and signals by Das, P

“…Using these results we derive a formulation of the pathwise F ̈ollmer-Itˆo calculus which is invariant with respect to the partition sequences. …”