Research interests

• 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)

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

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

• Mathematics of AI (neural networks, reinforcement learning)

Current and former PhD students

• Advisor for Patrik Nummi, University of Helsinki. Supervised by Tuomo Kuusi.

• Advisor for Nourhan Shafik, Aalto University School of Science. Dissertation: On complicated dependency structures (October 2023). Supervised by Pauliina Ilmonen.

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

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

• Advisor for Zhe Chen, Aalto University School of Science. Dissertation: On Pathwise Stochastic Integration of Processes with Unbounded Power Variation (March 2016). Supervised by Lasse Leskelä.

Postdocs

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

Recent preprints

See my Arxiv page. 

Journal articles

• Avelin, B., Julin, V., Viitasaari, L. (2023). Geometric characterisation of the Eyring-Kramers formula. Accepted for publication in Communications in mathematical physics.

• 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).