Author Archives: Fabrice Baudoin

Lecture 6. Rough paths Fall 2017

In the previous lecture we defined the Young’s integral when and with . The integral path has then a bounded -variation. Now, if is a Lipschitz map, then the integral, is only defined when , that is for . With … Continue reading

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HW3. MA3160 Fall 2017

Exercise 1. Two dice are simultaneously rolled. For each pair of events defined below, compute if they are independent or not. (a) A1 ={thesumis7},B1 ={thefirstdielandsa3}. (b) A2 = {the sum is 9}, B2 = {the second die lands a 3}. (c) … Continue reading

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Lecture 5. Rough paths. Fall 2017

In this lecture we define the Young‘s integral when and with . The cornerstone is the following Young-Loeve estimate. Theorem: Let and . Consider now with . The following estimate holds: for , Proof: For , let us define We … Continue reading

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MA3160. Fall 2017. HW2

Exercise 1. Suppose that A and B are pairwise disjoint events for which P(A) = 0.3 and P(B) = 0.5.   What is the probability that B occurs but A does not?   What is the probability that neither A nor … Continue reading

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Lecture 4. Rough paths. Fall 2017

Our next goal in this course is to define an integral that can be used to integrate rougher paths than bounded variation. As we are going to see, Young’s integration theory allows to define as soon as has finite -variation … Continue reading

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Lecture 3 Rough paths. Fall 2017

Let and let be a Lipschitz continuous map. In order to analyse the solution of the differential equation, and make the geometry enter into the scene, it is convenient to see as a collection of vector fields , where the … Continue reading

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Rough paths theory Fall 2017. Lecture 2

In this lecture we establish the basic existence and uniqueness results concerning differential equations driven by bounded variation paths and prove the continuity in the 1-variation topology of the solution of an equation with respect to the driving signal. Theorem: … Continue reading

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