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“TOPICS IN STOCHASTIC ANALYSIS: MALLIAVIN CALCULUS”

Malliavin calculus, also known as the stochastic calculus of variations, provides tools for analyzing the smoothness of functionals of stochastic processes. It is particularly useful in understanding the regularity properties of solutions to stochastic differential equations (SDEs), including those arising in mathematical finance. For example, Malliavin calculus can be used to study the smoothness of the density, which is crucial for practical applications like numerical simulations and approximations of prices and sensitivities.