Department of Mathematics and Statistics


Probability theory (or stochastics) is the mathematical theory of randomness. It is a major research subject in pure mathematics where probability interacts with other fields, like partial differential equations and real and complex analysis. But it is also an important part of applied mathematics as stochastics analyses and models systems and processes. Therefore stochastics is used in many disciplines such as statistics, physics, economics and computer science.
In our days there is an increasing demand in the society for mathematicians with a strong knowledge in probability theory, a good understanding of applications of stochastics and a receptive attitude to new theories and problems. At our university, the research in stochastics focuses on stochastic analysis and its interactions with analysis and to applications in complexity theory, numerics and statistics.

    Research -- Teaching -- Lecture notes -- Events


Stefan Geiss Professor
Stefan Geiss
Christel Geiss Senior lecturer
Christel Geiss
Anni Toivola University teacher
Anni Laitinen
Eija Laukkarinen

Postdoctoral researcher
Eija Laukkarinen

Postdoctoral researcher
Juha Ylinen
Matti Vihola

Academy research fellow
Matti Vihola

AnttiLuoto1.png Doctoral student
Antti Luoto
Jordan Franks Doctoral student
Jordan Franks
Henri Ylinen3.png Doctoral student
Henri Ylinen
Thuan Nguyen2.png Doctoral student
Thuan Nguyen


Collaborating members in the Statistics research group: Salme Kärkkäinen, Juha Karvanen, Jukka Nyblom, Antti Penttinen

Former members: Heikki Seppälä, Rainer Avikainen, Mika Hujo, Mikko Kuronen, Lasse Leskelä, Teemu Pennanen, Eero Saksman


The main research topics of the Stochastics group are

  • Stochastic Analysis on the Itô-Wiener space (Brownian motion and Lévy Processes)
    • Backward Stochastic Differential Equations
    • Calculus of Variations
    • Besov Spaces and Interpolation Theory
    • Harmonic Analysis
    • Approximation Theory for Stochastic Processes
  • Probability in Banach Spaces
  • Probability and Statistical Applications
    • Monte Carlo methods
    • Markov Chains
    • Stochastic Approximation

    Some events related to our research interests


    Publications of the group can be found on the arXiv preprint server and the TUTKA database. The most up-to-date information is available on the members' personal web pages.

    Selected articles

    • E. Laukkarinen. A note on Malliavin smoothness on the Lévy space. Electronic Communications in Probability 22(34): 1-12, 2017.
    • F. Baumgartner and S. Geiss. Permutation invariant functionals of Lévy processes. Transactions AMS May, 2017.
    • L. Leskelä and M. Vihola Conditional convex orders and measurable martingale couplings, Bernoulli, 23(4A):2784–2807, 2017. doi:10.3150/16-BEJ827
    • C. Andrieu and M. Vihola Establishing some order amongst exact approximations of MCMCs, Annals of Applied Probability. 26(5):2661–2696, 2016. doi:10.1214/15-AAP1158
    • B. Bouchard, S. Geiss and E. Gobet. First time to exit of a continuous Itô process: general moment estimates and L1-convergence rate for discrete time approximations. Bernoulli 23(3):1631-1662, 2017.
    • C. Geiss and C. Labart. Simulation of BSDEs with jumps by Wiener Chaos Expansion.
      Stoch. Proc. Appl. 126, pp.2123-2162, 2016.
    • C. Geiss and A. Steinicke. Malliavin derivative of random functions and applications to Lévy driven BSDEs.
      Electron. J. Probab. 21 pp. 28, 2016.
    • C. Andrieu and M. Vihola. Convergence properties of pseudo-marginal Markov chain Monte Carlo algorithmsAnnals of Applied Probability, 25(2):1030–1077, 2015.
    • S. Geiss and A. Toivola. On fractional smoothness and Lp-approximation on the Gaussian space. Annals of Probability, Vol. 43, pp. 605-638, 2015.
    • S. Geiss and E. Gobet. Fractional smoothness of functionals of diffusion processes under a change of measure. Electronic Communications in Probability, Vol.19(35), 2014.
    • C. Geiss, S. Geiss and E. Laukkarinen. A note on Malliavin fractional smoothness for Lévy processes and approximation. Potential Analysis 39, pp.203-230, 2013.
    • C. Geiss, S. Geiss and E. Gobet. Generalized fractional smoothness and Lp-variation of BSDEs with non-Lipschitz terminal conditions. Stochastic Processes and their Applications 122, pp.2078-2116, 2012.


    We teach undergraduate and graduate courses in stochastics. The undergraduate courses are given in Finnish or in English. The advanced stochastics courses are eligible as a basis for the SHV degree in insurance mathematics.

    Lecture notes

    Bachelor topics

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    Spring 2018 (courses 2017-2020)

    • MATS442 Stochastic Simulation, 4 ECTS (17.1.18 - 21.3.18) - Korppi
    • MATS352 Stochastic Analysis, 5 ECTS (10.1.2018 - 7.3.2018) - Korppi
    • MATS260 Probability Theory 1, 5 ECTS (16.1.2018 - 14.3.2018) - Korppi
    • MATA271 Stochastic Models, 4 ECTS (13.3.2018 - 2.5.2018) - Korppi
    • MATS2300 Models in Financial Mathematics, 5 ECTS (14.3.2018 - 16.5.2018) - Korppi

    Autumn 2017

    • MATA280 Foundations of Stochastics, 5 ECTS (23.10.17 - 20.12.17) - Korppi
    • MATS262 Probability Theory 2, 5 ECTS (4.9.2017 - 8.11.2017) - Korppi
    • MATS280 Risk Theory, 5 ECTS (4.9.2017 - 1.11.2017) - Korppi
    • MATS254 Stochastic processes, 4 ECTS (23.10.2017 - 7.12.2017)- Korppi
    • MATS256 Advanced Markov Processes, 5 ECTS (25.10.2017 - 18.12.2017)- Korppi

    Spring 2017

    Autumn 2016

    Autumn 2014-Spring 2016 download