Research interests

In my research, I am always enthusiastic to learn new research and application areas that involve randomness, and my current and past research reflects this by combining various disciplines of statistics and probability. My research covers topics and intersections of:

• Mathematical statistics (Limit theorems, statistical inference in stochastic models, time series analysis, prediction, missing data, functional data analysis, independent component analysis, extreme value theory)

• Finite sample bounds in statistics (Total variation bounds, Concentration)

• Operations research (Stochastic optimization and statistical methodology applied e.g. in biology, epidemiology, forest management)

• Mathematical finance (Interest rate models, Stochastic volatility models)

• Mathematics of AI (neural networks, reinforcement learning)

• Stochastic analysis (Gaussian processes, integration theory, stochastic partial and backward differential equations, general theory of stochastic processes)

• Non-random stochastic analysis (pathwise analysis, fractional calculus, PDEs)

Current and former PhD students

• Anna-Mariya Otsetova, Aalto University School of Science (jointly with J. Kinnunen).

• Mahdi Dehshiri, Aalto University School of Business (jointly with S. Särkkä).

• Chenyang Bao, Aalto University School of Business (jointly with P. Malo). 

• Milla Laurikkala, Aalto University School of Science (jointly with P. Ilmonen).

• Aron Persson, Uppsala University (jointly with B. Avelin, T. Ekholm, J.-L. Figueras).

• Patrik Nummi, University of Helsinki (jointly with T. Kuusi). Dissertation: Gaussian Fields and Equations of Divergence-form: Continuity, Boundedness, and Approximations (February 2025).

• Nourhan Shafik, Aalto University School of Science (jointly with P. Ilmonen). Dissertation: On complicated dependency structures (October 2023). 

• Sami Helander, Aalto University School of Science (jointly with P. Ilmonen). Dissertation: New approaches for analysing functional data - a focus on shape (August 2022). 

• Marko Voutilainen, Aalto University School of Science (jointly with P. Ilmonen). Dissertation: New approaches for modeling and estimation of discrete and continuous time stationary processes (December 2020).

• Zhe Chen, Aalto University School of Science (jointly with L. Leskelä). Dissertation: On Pathwise Stochastic Integration of Processes with Unbounded Power Variation (March 2016). 

Postdocs

• Valentin Garino, Uppsala University (September 2022 - August 2024).

Recent preprints

See my Arxiv page. 

Journal articles

• Avelin, B., Nummi, P., Kuusi, T., Saksman, E., Tölle, J., Viitasaari, L. (2025). Renormalized stochastic pressure equation with log-correlated Gaussian coefficients. Accepted for publication in Journal of Differential Equations.

• Hinz, M., Tölle, J., Viitasaari, L. (2025). Variability and the existence of rough integrals with irregular coefficients. Electronic Communications in Probability 30, no. 7, 1--12.

• Sottinen, T., Sönmez, E., Viitasaari, L. (2024). On the existence and regularity of local times. Electronic Journal of Probability 29, 1-27.

• Pere, J., Ilmonen, P., Viitasaari, L. (2024). On extreme quantile region estimation under heavy-tailed elliptical distributions. Journal of Multivariate Analysis 202:105314.

• Virta, J., Lietzen, N., Viitasaari, L., Ilmonen, P. (2024). Latent model extreme value index estimation. Journal of Multivariate Analysis 202:105300.

• Dufitinema, J., Shokrollahi, F., Sottinen, T., Viitasaari, L. (2024). Long-range dependent completely correlated mixed fractional Brownian motion. Stochastic Processes and their Applications 170:104289.

• Nummi, P., Viitasaari, L. (2024). Necessary and sufficient conditions for continuity of hypercontractive processes and fields. Statistics and Probability Letters 208:110049.

• Voutilainen, M., Ilmonen, P., Viitasaari, L. (2024). On Lamperti transform and AR(1) type characterisations of discrete random fields. Accepted for publication in Theory of Probability and Mathematical Statistics.

• Avelin, B., Julin, V., Viitasaari, L. (2023). Geometric characterisation of the Eyring-Kramers formula. Communications in mathematical physics 404:401-437.

• Shafik N., Ilmonen, P., Viitasaari, L., Sarkeala, T., Heinävaara, S. (2023). Flexible transition probability model for assessing cost-effectiveness of breast cancer screening extension to include women aged 45-49 and 70-74. PLos One, 18(6):e0287486. DOI: 10.1371/journal.pone.0287486.

• Azmoodeh, E., Ilmonen, P., Shafik, N., Sottinen, T., Viitasaari, L. (2023). On sharp rate of convergence for discretisation of integrals driven by fractional Brownian motions and related processes with discontinuous integrands. Journal of Theoretical Probability. DOI: https://doi.org./10.1007/s10959-023-01272-7

• Torres, S., Viitasaari, L. (2023). Stochastic differential equations with discontinuous diffusion coefficients. Accepted in Theory of Probability and Mathematical Statistics.

• Tahvonen, O., Suominen, A., Malo, P., Viitasaari, L., Parkatti, V.-P. (2022). Optimizing high-dimensional stochastic forestry via reinforcement learning. Journal of Economic Dynamics and Control. DOI: https://doi.org/10.1016/j.jedc.2022.104553.

• Hinz, M., Tölle, J., Viitasaari, L. (2022). Variability of paths and differential equations with BV-coefficients. Accepted for publication in Ann. Inst. H. Poincare Probab. Statist.

• Voutilainen, M., Ilmonen, P., Viitasaari, L., Lietzen, N. (2022). Note on asymptotic behaviour of spatial sign autocovariance matrices. Statistics and Probability Letters, 192, 109679.

• Viitasaari, L., Zeng, C. (2022). Stationary Wong-Zakai Approximation of Fractional Brownian Motion and Stochastic Differential Equations with Noise Perturbations. Fractal and Fractional, 6(6): 303.

• Hinz, M., Tölle, J., Viitasaari, L. (2022). Sobolev regularity of occupation measures and paths, variability and compositions. Electronic Journal of Probability, 27(73): 1--29.

• Helander, S., Laketa, P., Ilmonen, P., Nagy, S., Van Bever, G., Viitasaari, L. (2022). Integrated shape-sensitive functional metrics. Journal of Multivariate Analysis 189, 104880.

• Assaad, O., Nualart, D., Tudor, C.A., Viitasaari, L. (2022). Quantitative normal approximations for the stochastic fractional heat equation. Stochastics and Partial Differential Equations: Analysis and Computations, 10: 223--264. DOI: https://doi.org/10.1007/s40072-021-00198-7.

• Bertin, K., Torres, S., Viitasaari, L. (2021). Least square estimators in linear regression models under negatively superadditive dependent random observations. Statistics, 55(5): 1018-1034..

• Avelin, B., Viitasaari, L. (2021). On existence and uniqueness of the solution for stochastic partial differential equations. Theory of Probability and Mathematical Statistics, 104: 49-60.

• Voutilainen, M., Viitasaari, L., Ilmonen, P., Torres, S., Tudor, C. (2021). Vector-valued Generalised Ornstein-Uhlenbeck Processes. Accepted for publication in Scandinavian Journal of Statistics. DOI: https://doi.org/10.1111/sjos.12552.

• Arvonen, M., Raittinen, P., Niemenoja, O., Ilmonen, P., Riihijärvi, S., Särkkä, S., Viitasaari, L. (2021). Nationwide infection control strategy lowers seasonal respiratory infection rate: occupational health care perspective during COVID-19 epidemic in Finland. Infectious Diseases. DOI: https://doi.org/10.1080/23744235.2021.1944661.

• Lietzen, N., Viitasaari, L., Ilmonen, P. (2021). Modeling temporally uncorrelated components of complex-valued stationary processes. Modern Stochastics: Theory and Applications, 8(4): 475--508.

• Malo, P., Tahvonen, O., Suominen, A., Back, P., Viitasaari L. (2021). Reinforcement Learning in Optimizing Forest Management. Canadian Journal of Forest Research. DOI: https://doi.org/10.1139/cjfr-2020-0447. 

• Kerchev, G., Nourdin, I., Saksman, E., Viitasaari, L. (2021). Local times and sample path properties of the Rosenblatt process. Stochastic Processes and Their Applications, 131: 498--522. 

• Nagy, S., Helander, S., van Bever, G., Viitasaari, L., Ilmonen, P. (2020). Flexible integrated functional depths. Bernoulli, 27(1): 673--701. 

• Huang, J., Nualart, D., Viitasaari, L. (2020). A Central Limit Theorem for the stochastic heat equation. Stochastic Processes and Their Applications. DOI: https://doi.org/10.1016/j.spa.2020.07.010. 

• Aalto, A., Viitasaari, L., Ilmonen, P., Mombaerts, L., Goncalves, J. (2020). Gene regulatory network inference from sparsely sampled noisy data. Nature Communications, 11:3493. DOI: 10.1038/s41467-020-17217-1. 

• Forde, M., Smith, B., Viitasaari, L. (2020). Rough volatility and CGMY jumps with a finite history and the rough Heston model -- small-time asymptotics in the $k\sqrt{t}$ regime. Quantitative Finance. DOI: https://doi.org/10.1080/14697688.2020.1790634. 

• Ilmonen, P., Torres, S., Tudor, C., Viitasaari, L., Voutilainen, M. (2020). On the ARCH model with stationary liquidity. Metrika. DOI: https://doi.org/10.1007/s00184-020-00779-x.

• Ilmonen, P., Torres, S., Viitasaari, L. (2020). Oscillating Gaussian processes. Statistical Inference for Stochastic Processes, 23: 571--593. 

• Hyytiä, E., Righter, R., Virtamo, J., Viitasaari, L. (2020). On Value Functions for FCFS Queues with Batch Arrivals and General Cost Structures. Performance Evaluation, 138. DOI: https://doi.org/10.1016/j.peva.2020.102083. 

• Ilmonen, P., Viitasaari, L. (2020). On modeling a class of weakly stationary processes. Frontiers in Applied Mathematics and Statistics. DOI: https://doi.org/10.3389/fams.2019.00068 (invited contribution). 

• Azmoodeh, E., Sottinen, T., Tudor, C.A., Lauri Viitasaari, L. (2020). Integration-by-Parts Characterizations of Gaussian Processes. Collectanea Mathematica. DOI: https://doi.org/10.1007/s13348-019-00278-x. 

• Sottinen, T., Viitasaari, L. (2020). Prediction Law of Mixed Gaussian Volterra Processes. Statistics and Probability Letters, 156. DOI: https://doi.org/10.1016/j.spl.2019.108594. 

• Ilmonen, P., Viitasaari, L. (2019). A note on distributions in the second chaos. Symmetry, 11(12). DOI: https://doi.org/10.3390/sym11121487 (invited contribution). 

• Bajja, S., Es-Sebaiy, K., Viitasaari, L. (2019). Volatility estimation in fractional Ornstein-Uhlenbeck models. Stochastic Models. DOI: https://doi.org/10.1080/15326349.2019.1692668. 

• Huang, J., Nualart, D., Viitasaari, L., Zheng, G. (2019). Gaussian fluctuations for the stochastic heat equation with colored noise. Stochastics and Partial Differential Equations: Analysis and Computations. DOI: https://doi.org/10.1007/s40072-019-00149-3. 

• Viitasaari, L. (2019). Sufficient and necessary conditions for limit theorems for quadratic variations of Gaussian sequences. Probability Surveys, 16: 62--98. 

• Voutilainen, M., Viitasaari, L., Ilmonen, P. (2019). Note on AR(1)-characterisation of stationary processes and model fitting. Modern Stochastics: Theory and Applications, 6(2): 195--207. 

• Chen, Z., Leskelä, L., Viitasaari, L. (2019). Pathwise Stieltjes integrals of discontinuously evaluated stochastic processes. Stochastic Processes and Their Applications, 129(8): 2723--2757. 

• Sottinen, T., Viitasaari, L. (2018). Conditional-Mean Hedging Under Transaction Costs in Gaussian Models. International Journal of Theoretical and Applied Finance. DOI: https://doi.org/10.1142/S0219024918500152. 

• Sottinen, T., Viitasaari, L. (2018). Transfer Principle for nth Order Fractional Brownian Motion with Applications to Prediction and Equivalence in Law. Theory of Probability and Mathematical Statistics, 98: 188--204. 

• Sottinen, T., Viitasaari, L. (2018). Parameter Estimation for the Langevin Equation with Stationary-Increment Gaussian Noise. Statistical Inference for Stochastic Processes, 21(3): 569--601. 

• Voutilainen, M., Viitasaari, L., Ilmonen, P. (2017). On model fitting and estimation of strictly stationary processes. Modern Stochastics: Theory and Applications, 4(4): 381--406. 

• Sottinen, T., Viitasaari, L. (2017). Prediction law of fractional Brownian motion. Statistics and Probability Letters, 129: 155--166. 

• Bender, C., Viitasaari, L. (2017). A general non-existence result for linear BSDEs driven by Gaussian processes. Stochastic Processes and Their Applications, 127(4): 1204--1233. 

• Bajja, S., Es-Sebaiy, K., Viitasaari, L. (2017). Least squares estimator of fractional Ornstein Uhlenbeck processes with periodic mean. Journal of the Korean Statistical Society, 46(4): 608--622. 

• Sottinen T., Viitasaari, L. (2016). Stochastic analysis of Gaussian processes via Fredholm representation. International Journal of Stochastic Analysis. DOI:10.1155/2016/8694365. 

• Viitasaari, L. (2016). Representation of stationary and stationary increment processes via Langevin equation and self-similar processes. Statistics and Probability Letters, 115: 45--53. 

• Sottinen, T., Viitasaari, L. (2016). Pathwise integrals and It\^o-Tanaka Formula for Gaussian processes. Journal of Theoretical Probability, 29(2): 590--616. 

• Viitasaari, L. (2016). Integral representation of random variables with respect to Gaussian processes. Bernoulli 22(1):  376--395. 

• Azmoodeh, E., Viitasaari, L. (2015). Parameter estimation based on discrete observations of fractional Ornstein-Uhlenbeck process of the second kind. Statistical Inference for Stochastic Processes, 18(3): 205--227. 

• Azmoodeh, E., Sottinen, T., Viitasaari, L. (2015). Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian--fractional Brownian model. Modern Stochastics: Theory and Applications 2(1): 29--49. 

• Azmoodeh, E., Viitasaari, L. (2015). Rate of convergence for discretization of integrals with respect to Fractional Brownian motion. Journal of Theoretical Probability, 28(1): 396--422. 

• Viitasaari, L. (2015). A remark on option prices with call prices. Journal of Mathematical Sciences, 2(3): 97--105. 

• Shevchenko, G., Viitasaari, L. (2014). Integral representation with adapted continuous integrand with respect to fractional Brownian motion. Stochastic Analysis and Applications 32: 1--10. 

• Azmoodeh, E., Sottinen, T., Viitasaari, L., Yazigi, A. (2014). Necessary and sufficient conditions for H\"older continuity of Gaussian processes. Statistics and Probability Letters 94: 230--235. 

• Talponen, J., Viitasaari, L. (2014). Note on multidimensional Breeden-Litzenberger representation for state price densities. Mathematics and Financial Economics 8: 153--157.

Conference articles (peer-reviewed)

• Bajja, S., Es-Sebaiy, K., Viitasaari, L. (2018). Limit theorems for quadratic variations of the Lei-Nualart process. In: Silvestrov, S., Malyarenko, A., Rancic, M. (eds.) Stochastic Processes and Applications. SPAS 2017. Springer Proceedings in Mathematics & Statistics, 271, Springer. DOI: https://doi.org/10.1007/978-3-030-02825-15. 

• Hyytiä, E., Righter, R., Virtamo, J., Viitasaari, L. (2017). Value (generating) functions for the M^X/G/1 queue. 29th International Teletraffic Congress (ITC 29), Genoa, pp. 232--240. DOI: 10.23919/ITC.2017.8064360. 

• Sottinen, T., Viitasaari, L. (2015). Fredholm representation of multi-parameter Gaussian processes with applications to equivalence in law and series expansions. Modern Stochastics: Theory and Applications 2(3): 287--295 (proceedings of the PRESTO-2015 conference). 

• Shevchenko, G., Viitasaari, L. (2015). Adapted integral representations of random variables. Int. J. Mod. Phys. Conf. Ser. 36. DOI: 10.1142/S2010194515600046 (proceedings of the JAGNA-workshop).

Review articles (peer-reviewed)

• Bender, C., Viitasaari, L. (2016). Fractional Brownian motion in financial modeling. Wiley StatsRef: Statistics Reference Online (stat07865).