Conference Agenda
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Daily Overview |
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Pl 3: Plenary Lecture
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Integration: Old and New TU and WIAS Berlin
This talk starts with basic Riemann vs Lebesgue integration, turning then to stochastic and rough integration. We develop the concept of rough Itô processes, which extend stochastic calculus to accommodate rough stochastic differential equations (SDEs) and their mean-field counterparts. These structures provide a natural setting for stochastic modelling under partial conditioning of the noise. Concrete applications include non-linear filtering, pathwise stochastic control theory, local stochastic volatility modelling, and interacting particle systems with common noise. In Markovian situations our methods have led to some significant advances in the analsysis of non-linear stochastic partial differential equations.
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