by Alan Bain
Number of pages: 99
These notes provide a very informal introduction to Stochastic Calculus, and especially to the Ito integral and some of its applications. The text concentrates on the parts of the course which the author found hard, there is often little or no comment on more standard matters.
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The aim is to introduce the basic problems of non-linear PDEs with stochastic and irregular terms. We explain how it is possible to handle them using two main techniques: the notion of energy solutions and that of paracontrolled distributions.
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