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...Notes on malliavin calculus joe jackson may these are lecture for a summer mini course first we will review stochastic integration and introduce the basic operators of wewill then take detour to study some sde theory see connection between sdes cauchy problem finally explain how can be applied give probabilistic proof h ormander s theorem sections borrow heavily from book introduction by david nualart much section i learned an expository paper martin hairer titled contents setup wiener space denite it o integral indenite stratonovich derivative its adjoint denitions interpreting d tools dierential equations existence uniqueness solution densities results in main criteria smooth statement intuition about condition let f p probability x r random variable would like talk but this is hopeless without more analytical structure luckily many variables interest dened as functionals brownian motion which case might well denition where c borel algebra there unique measure such that process bt t ...