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Mathematics Colloquium

Rama Cont
University of Oxford

Title: Causal functional calculus
Date: Friday, September 17, 2021
Place and Time: Zoom, 3:05-3:55 pm


Ito's Stochastic calculus is traditionally viewed as a calculus for functions of stochastic processes, but may be alternatively seen as a calculus for causal functionals of systems with irregular trajectories of a specific type. We show how the main ingredients of the Ito calculus may be developed in a purely analytical framework, free of any probabilistic ingredients or assumptions, and describe a causal functional calculus which extends the Newton-Leibniz differential calculus to functionals of systems with rough trajectories of arbitrary irregularity [1, 2] going well beyond the setting of Ito's Stochastic calculus.

[1] H Chiu, R Cont (2020) Causal Functional Calculus, https://arxiv.org/abs/1912.07951
[2] R Cont, N Perkowski (2019) Pathwise integration and change of variable formulas for continuous paths with arbitrary regularity, Transactions of the American Mathematical Society (Series B), Volume 6, 161-186.