[ABE-L] Seminários de Probabilidade (online) -- IM-UFRJ - 24/08

[Maria Eulalia Vares]

* Probability Webinar  -- IM-UFRJ  - 24/08*


Dear colleagues,

Our next online seminar will be held next Monday, August 24, from *3 p.m.
to 4 p.m*. (Rio de Janeiro local time)

The GoogleMeet link for the seminars is:
https://meet.google.com/nxh-optr-wtq

Speaker:  Daniel  Yasumasa Takahashi  (UFRN)

Title: *Mixing rates for processes with long-memory*

Abstract:  Non-Markovian processes are ubiquitous, but they are much less
understood compared to Markov processes.  We model non-Markovianity using
probability kernels that can depend on its entire history. The continuity
rate characterizes how the dependence of kernel on the past decays. One key
question is to understand how the mixing rates and decay of correlation are
related to the continuity rate. Pollicot (2000) and Bressaud, Fernandez,
Galves (1999) showed that if the continuity rate decays as O(1/n^c), for c
> 1, then the correlation also decays as O(1/n^c). Johansson, Oberg,
Pollicott (2007) proved the uniqueness of the stationary measure compatible
with kernels with the continuity rate in O(1/n^c), for c > 1/2. Moreover,
Berger, Hoffman, Sidoravicius (2018) established that there are kennels
with multiple compatible measures whenever c < 1/2. Therefore, the natural
question is to understand the mixing rates and correlation decays when c is
in [1/2,1]. In this talk, I will exhibit upper bounds for the mixing rates
and correlation decays when the continuity rate decays as  O(1/n^c), for c
in (1/2,1].  If time allows, I will show how to apply the result to prove a
new weak invariance principle. This talk is based on joint work with
Christophe Gallesco.




All the talks are held in English.

Thanks for circulating this information.

Sincerely,

Organizers: Guilherme Ost and Maria Eulalia Vares
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