# Stochastics and statistics

Stochastic analysis and statistical modeling are key methodologies for analyzing random interactions in today's information systems. Our research group applies and develops methods in probability theory and mathematical statistics related to applications in communication and transportation networks, engineering, and natural sciences. The main research areas are: stochastic networks and queueing systems, asymptotic statistics, and random spatial structures.

## Teaching

We teach courses in probability and statistics at all levels. Many of the offered MSc courses are eligible as a basis for an SHV degree in insurance mathematics. PhD education in stochastics and statistics is coordinated by the Finnish Doctoral Education Network in Stochastics and Statistics (FDNSS).

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#### MSc/PhD courses 2016-2017

#### BSc courses 2016-2017

#### Basic courses 2016-2017

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## People

Affiliated postdocs: Steven Flores (University of Helsinki), Giancarlo Pastor (VTT Research Centre), Lauri Viitasaari (University of Saarbrücken).

Affiliated PhD students: Mikko Kuronen (University of Jyväskylä), Matias Leppisaari (Model IT), Eveliina Peltola (University of Helsinki), Mika Sirviö (Insurance Centre), Tarja Sirén (Financial Supervisory Authority).

Affiliated docents: Kari Eloranta, Teemu Pennanen (King's College London), Karl Sigman (Columbia University).

Aalto Stochastics mailing list

Aalto Stochastics Wiki

### Visitors

**Giancarlo Pastor Figueroa 1.3.2016–31.8.2017**

## Talks

- 3.11. 11:00 Jevgenijs Ivanovs (Aarhus University): Zooming in on a Lévy process at its supremum – M3 (M234)
Let M and τ be the supremum and its time of a Lévy process X on some finite time interval. It is shown that zooming in on X at its supremum, that is, considering (a η (X τ +t/η − M )) t∈R as η, a η → ∞, results in (ξ t ) t∈R constructed from two independent processes corresponding to some self-similar Lévy process S conditioned to stay positive and negative. This holds when X is in the domain of attraction of S under the zooming-in procedure as opposed to the classical zooming-out of Lamperti [1962]. As an application of this result we provide a limit theorem for the discretization errors in simulation of supremum and its time, which extends the result of Asmussen, Glynn, and Pitman [1995] for the Brownian motion.
In this talk I will aim at a general mathematical audience providing various illustrations of basic concepts.

- 1.11. 14:15 Matti Vihola (University of Jyväskylä): Unbiased estimators and multilevel Monte Carlo – M203
Multilevel Monte Carlo (MLMC) and recently proposed debiasing schemes are closely related methods for scenarios where exact simulation methods are difficult to implement, but biased estimators are available. An important application is inference with stochastic differential equation models, where the continuous-time process is difficult to simulate but time-discretized approximations are easy to implement.
A new general class of unbiased estimators is introduced, which admits earlier debiasing schemes as special cases, and accomodates new lower variance estimators based on stratification. The stratified schemes behave asymptotically like MLMC, both in terms of variance and cost, under general conditions --- essentially those that guarantee canonical square root rate of MLMC. This suggests that MLMC bias can often be eliminated entirely with small extra cost. The new schemes also admit optimisation criteria which are easy to implement in practice.
(The talk is based on arXiv:1512.01022)

- 31.10. 15:15 Hao Wu (University of Geneva): Arm Exponents for Ising and FK-Ising Model (further info) – M3 (M234)
The introduction of SLE by Oded Schramm provides mathematicians with a new tool to study critical lattice models.
In the first part of this talk, I will discuss critical planar percolation and explain how people use SLE to derive the arm
exponents of percolation. In the second part, I will introduce SLE and general formulae on arm exponents of SLE, and
show that these formulae give us various results on the arm exponents of critical planar Ising and FK-Ising models.
Finally, I will explain some related results and some open questions.

## Events

## Projects

## Selected publications

- J Barral, A Kupiainen, M Nikula, E Saksman, C Webb. Basic properties of critical lognormal multiplicative chaos.
*The Annals of* *Probability 43(5):2205-2249, 2015*.
- P Aalto, L Leskelä. Information spreading in a large population of active transmitters and passive receivers.
*SIAM Journal on Applied Mathematics* 75(5):1965–1982, 2015.
- E Azmoodeh, L Viitasaari. Rate of convergence for discretization of integrals with respect to fractional Brownian motion.
*Journal of Theoretical Probability*, 28(1):396-422, 2015.
- C Hongler, K Kytölä. Ising interfaces and free boundary conditions.
*Journal of the American Mathematical Society *26:1107–1189, 2013.
- P Ilmonen, D Paindaveine. Semiparametrically efficient inference based on signed ranks in symmetric independent component models.
*Annals of Statistics* 39(5):2448–2476, 2011.

## Alumni

Helena Aro (Etera)

Ehsan Azmoodeh (University of Luxembourg)

Zhe Chen

Milla Kibble (FIMM Institute for Molecular Medicine Finland)

Matti Kiiski (ETH Zürich)

Ilkka Mellin (University teacher emeritus)

Igor Morlanes (Stockholm University)

Amitava Mukherjee (XLRI- Xavier School of Management)

Ari-Pekka Perkkiö (Technische Universität Berlin)

Heikki Tikanmäki (Finnish Centre for Pensions)

Esko Valkeila (1951–2012)

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