From weighted estimates to change of law.
Connections for Women: Harmonic Analysis January 19, 2017 - January 20, 2017
Location: SLMath: Eisenbud Auditorium
weighted theory
probability
harmonic analysis
stochastic processes
martingales
57R22 - Topology of vector bundles and fiber bundles [See also 55Rxx]
57R25 - Vector fields, frame fields in differential topology
00B25 - Proceedings of conferences of miscellaneous specific interest
From Weighted Estimates To Change Of Law
We discuss historic aspects of 'sharp weighted estimates', notably its origins in simple probability spaces with dyadic filtrations. Some cornerstone results central to harmonic analysis will be mentioned in a historic fashion. The main part of the lecture returns to the probabilistic setting and stochastic analysis in filtered spaces with continuous time, arbitrary underlying measure and possible 'jumps'. It is proved - via two important methods from 'weights', Bellman and Sparse, that 'all' subordinate pairs of martingales have a sharp A_p bound. It is remarkable that in this generality, not even the boundedness of the maximal function seems to have been known - a fact that presents no difficulty at all with today's methods. This lecture should also serve as an introduction to techniques in 'weights' for those participating in the semester
Petermichl Notes
|
Download |
From Weighted Estimates To Change Of Law
H.264 Video |
04-Petermichl.mp4
|
Download |
Please report video problems to itsupport@slmath.org.
See more of our Streaming videos on our main VMath Videos page.