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Category Archives: Rough paths theory
My book which is published by the European Mathematical Society is now available. Diffusion Processes and Stochastic Calculus The content is partially based on the lecture notes in stochastic calculus and rough paths theory which are posted on this blog … Continue reading
For those who are interested, here are the notes corresponding to the lectures posted on this blog. All comments are welcome.
To conclude this course, we are going to provide an elementary proof of the Stroock–Varadhan support theorem which is based on rough paths theory. We first remind that the support of a random variable which defined on a metric space … Continue reading
Based on the results of the previous Lecture, it should come as no surprise that differential equations driven by the Brownian rough path should correspond to Stratonovitch differential equations. In this Lecture, we prove that it is indeed the case. … Continue reading
Since a -dimensional Brownian motion is a -rough path for , we know how to give a sense to the signature of the Brownian motion. In particular, the iterated integrals at any order of the Brownian motion are well defined … Continue reading
Our goal in the next two lectures will be to prove that rough differential equations driven by a Brownian motion seen as a -rough path, are nothing else but stochastic differential equations understood in the Stratonovitch sense. The proof of … Continue reading