Semester page for STK4290 - Spring 2017

In our last lesson on Thursday, 18. May, we discussed the reconstruction theorem of M. Hairer, which can be regarded as a generalization of the  Sewing Lemma. As an application of this theorem, we recovered the theorems of T. Lyons and M. Gubinelli on rough path integration as a particular case. See Ch. 13 in Friz, Hairer.

The lecture notes (part 5) on the construction of solutions to the KPZ equation via renormalization will be available on this website, soon.

May 26, 2017 11:48 PM

Muntlig eksamen på fredag, 9. juni, rom 637, NHA fra kl. 09:00 !

Eksamensform: Eksamenen som tar 45 minutter består av to deler:

1. Foredrag av fritt valg om et emne som er knyttet til røffstiteori. Foredragsemnet som foreslås skal meddeles meg senest 2 dager før eksamenen (via e-mail). Dessuten må emnet bli godkjent av meg. Foredraget skal vare i omtrent 20 minutter og fremføringsformen er opp til kandidatene (ved tavle med manus eller ikke, beamer,...).

 

2. Generelle spørsmål knyttet til røffstiteori.

Kap. 1, 2, 3 , 4.1, 4.2, 4.3 og Th. 4.6 i manuset mitt er kurspensum (eller se på de tilsvarende emnene i  boken til Friz, Hairer).

 

Manuset mitt er lagt ut på fagsiden.

Et sett av eksamensrelevante emner kan nedlastes her: emner

&nbs...

May 24, 2017 3:57 PM

In the last weeks we discussed the existence and uniqueness of rough differential equations, a priori estimates of solutions and the continuity of the Ito-Lyons map (see Ch. 8 in the Friz, Hairer). As an application of those results, we studied the link between solutions of Ito-SDE´s and RDE´s. Further we obtained the Wong-Zakai theorem on the approximation of SDE-solutions by means of solutions to ODE´s (see Ch. 9). In our next lesson (4. May) we aim at proving the support theorem of Stroock-Varadhan, which provides a characterization of the support of the distribution of Ito-SDE-solutions (see Ch. 9). Another application of the above mentioned results, we want to look at in the next lesson, pertains to the construction of solutions to a certain class of rough path and stochastic partial differential equations (see Ch. 12). Our plan is to start with Ch. 13 on an introduction to regularity structures as...

May 3, 2017 8:45 PM