in Advanced Probability
Novosibirsk State University, Sobolev Institute of Mathematics
March 12-16, 2018, Novosibirsk, Russian Federation
Point processes: basic concepts and limit theorems
Lecturer: Professor Sergey Zuev, Chalmers University of Technology, Sweden
We start by revising basic concepts of points processes (PP) and random measures in a general space: their definition, distribution, probability generating functional,Palm distribution.
We describe the main classes of PPs: Binomial, Poisson, Gibbs, cluster processes, branching random walk. Next, we establish specific properties of the Poisson PP and consider a few
applications based on the Poisson PP models in statistics and telecommunications. We then pass to the limit theorems involving superposition of PPs and characterise possible limits:
infinitely divisible, self-decomposable and stable PPs. If time allows, we finish by simulation methods and statistical inference.
A two-part lecture series, on Levy processes and on exchangeability
Lecturer: Professor Takis Konstantopoulos, Uppsala University, Sweden
In these lectures, I plan to cover two topics:
- The basic theory of Levy processes (or processes with stationary and independent increments).
This class of stochastic processes originated in the theory of addition of random variables (Kolmogorov, Gnedenko, Levy, among others).
I will include an exposition of the Wiener-Hopf factorization, the theory of hitting times and fluctuation. I will also discuss some applications, depending on time and interest.
I will give emphasis to probabilistic proofs, as much as possible.
- The theory of symmetry and exchangeability. I will review some concepts of ergodic theory and proceed to show the Ryll-Nardzewski approach to de Finetti's theorem.
The theory is fundamental to the foundation of Bayesian statistics. I will also include a discussion of finite exchangeability and symmetry.
All participants are encouraged to make a poster presentation about their research work during the evening scientific session of the School.
There's no thematic limitation on the topic of the presentation as long as it includes probabilistic formulation or methods.
Best presentations will be recommended for publication in the journal Siberian Journal of Pure and Applied Mathematics.
The English translation of this journal is provided by the Journal of Mathematical Sciences.
10:00 - 14:00
14.00 - 15.30
15:30 - 15:50
15.50 - 17.20
17.20 - 18.00
If you wish to register as a participant of our spring school please contact us via e-mail: sunakdb [at] gmail.com
- Sergey Foss (Novosibirsk, Edinburgh)
- Mikhail Chebunin (Novosibirsk): chebuninmikhail [at] gmail.com
- Anton Tarasenko (Novosibirsk): sunakdb [at] gmail.com
The School will take place at the Novosibirsk State University, room 4109.
The postal address: 1, Pirogova str., Novosibirsk, 630090, Russia.
There's two options we can recommend:
- The Golden Valley Hotel (Zolotaya Dolina).
Hotel rates are 1800-2800 RUB per night.
Building is located in the very heart of Akademgorodok, about 10 min walking distance from the Sobolev Institute of Mathematics.
- The hostel of NSU. Accommodation prices are essentially lower. If you're interested in this option please contact us via email: chebuninmikhail [at] gmail.com.
Public transport in Novosibirsk includes bus, minibus, tram and subway with fares varying between 20 and 50 RUB for a single journey.
Akademgorogok is situated 40 km from the Tolmachevo Airport (50-60 minutes by taxi, taxi price appr. 700 ‐ 750 RUB, see e.g. http://novosibirsk.rutaxi.ru/en/index.html
VAT and Tipping:
VAT and tips are included in prices. It is not customary to tip taxi drivers.
Shops are usually open 7 days a week from 9am/10am to 7pm/9pm. Food stores are open until 10pm/11pm.
The voltage in Russia is 220 AC (50 Hz).