From Spectral Gaps to Particle Filters

Reading University, September 17-18, 2013



A very important technique in the analysis of stochastic systems is to investigate the properties of associated transfer operators. Generally speaking, they determine to a large extent the long term behaviour of the system, such as rates of decay and de-correlation, as well as other ergodic or mixing properties. Therefore, the understanding of transfer operators and their analytic properties lies at the interface of functional analysis, stochastics, dynamics, and statistical methodology such as Monte Carlo and similar methods. In problems such as nonlinear filtering, positive (random) operators appear directly in the filter dynamics, and again their spectral properties play an important role in the long term behaviour of the filter. Furthermore, when approximating the optimal filter, for example by particle filters, error bounds have successfully been obtained by using stability properties of the filter operator. On the other hand, positive operators have also been investigated for their own sake and on a purely analytic basis, independent from stochastic processes.

This workshop is designed to provide a forum to exchange ideas and talk about new developments concerning the analytical aspects of transfer operators on the one side and applications to stochastic processes and statistical methodology on the other side. Consequently, the range of speakers will encompass people with more foundational expertise in the theory of transfer operators, as well as people doing more applied research but with a strong interest in the theory behind it. New mathematical problems arising from specific but important applications (such as from atmospheric dynamics, for example) are also expected to be discussed.

Programme and schedule:

This workshop will be over two consecutive days, with a slightly different focus for each day. The first day will be more concerned with the analysis of transfer operators, while on the second day we focus on applications in stochastic and dynamical systems.

See also the preliminary workshop schedule and the list of speakers and abstracts.

Time and venue:

The workshop will take place at the Nike Lecture Theatre, Agriculture Building, University of Reading (see here for directions to the workshop venue). If you come by car or taxi, you have to use the Earley Gate entrance; postcode RG6 7BE. GPS co-ordinates for the venue are Lat N51 26.3000 Lon W 0 56.133

Host Institution: Department of Mathematics and Statistics, University of Reading, England (see here for directions to our department).



The Cedars Hotel (on campus)

Hillingdon Prince (15-minute walk)

Great Expectations (25-minute walk)


If you'd like to attend, email the organizer at Registration fee: GBP 15GBP per diem.


Jochen Broecker, Richard Everitt, Martin Kolb and Mladen Savov.