Past Stochastic Analysis Seminar

21 November 2016
15:45
YILIN WANG
Abstract

We study some features of the energy of a deterministic chordal Loewner chain, which is defined as the Dirichlet energy of its driving function in a very directional way. Using an interpretation of this energy as a large deviation rate function for SLE_k as k goes to 0, we show that the energy of a deterministic curve from one boundary point A of a simply connected domain D to another boundary point B, is equal to the energy of its time-reversal i.e. of the same curve but viewed as going from B to A in D. In particular it measures how far does the chord differ from the hyperbolic geodesic. I will also discuss the relation between the energy of the curve with its regularity, some questions are still open. If time allows, I will present the Loewner energy for loops on the Riemann sphere, and open questions related to it as well.


 

  • Stochastic Analysis Seminar
21 November 2016
14:15
RICHARD SAMWORTH
Abstract

The class of log-concave densities on $\mathbb{R}^d$ is a very natural infinite-dimensional generalisation of the class of Gaussian densities.  I will show that it also allows the statistician to have the best of both the parametric and nonparametric worlds, in that one can obtain a fully automatic density estimator in the class (via maximum likelihood), with no tuning parameters to choose.  I'll discuss its computation, methodological consequences and theoretical properties, and in particular very recent results on minimax rates of convergence and adaptation.

 

  • Stochastic Analysis Seminar
14 November 2016
15:45
DAVID PROEMEL
Abstract

One of the central results in rough path theory is the local Lipschitz continuity of the solution map of a controlled differential equation called Ito-Lyons map. This continuity statement was obtained by T. Lyons in a q-variation resp. 1/q-Hölder type (rough path) metrics for any regularity 1/q>0. We extend this to a new class of Besov-Nikolskii type metrics with arbitrary regularity 1/q and integrability p, which particularly covers the aforementioned results as special cases. This talk is based on a joint work with Peter K. Friz.

 

  • Stochastic Analysis Seminar

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