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Tommi Sottinen - Research

Research interests

Fractional, Gaussian, self-similar, and quadratic variation processes; stochastic analysis; statistics for stochastic processes; stochastic simulation; mathematical finance; financial engineering.

Publications

    Refereed publications

  1. Sottinen, T. (2001) Fractional Brownian motion, random walks and binary market models. Finance and Stochastics 5, no. 3, 343-355.
  2. Kozachenko, Yu., Sottinen, T. and Vasylyk, O. (2002) Weakly Self-similar processes with stationary increments in the spaces SSub_\phi(\Omega). Theory of Probability and Mathematical Statistics 65, 77-88 .
  3. Kozachenko, Yu., Vasylyk, O. and Sottinen, T. (2002) Path Space Large Deviations of a Large Buffer with Gaussian Input Traffic. Queueing Systems 42, no. 2, 113-129.
  4. Sottinen, T. and Valkeila, E. (2003) On arbitrage and replication in the Fractional Black-Scholes pricing model. Statistics & Risk Modeling 21, 93-107.
  5. Gilsing, H. and Sottinen, T. (2003) Power series expansions for fractional Brownian motions. Theory of Stochastic Processes Vol. 9 (25), no. 3-4 (Proceedings of Seventh International School on Mathematical and Statistical Methods in Economics, Finance and Insurance), 38-49.
  6. Sottinen, T. (2003) Fractional Brownian motion in finance and queueing. Ph.D. Thesis, University of Helsinki.
  7. Sottinen, T. (2004) On Gaussian processes equivalent in law to fractional Brownian motion. Journal of Theoretical Probability 17, no. 2, 309-325.
  8. Kozachenko, Yu., Sottinen, T. and Vasylyk, O. (2005) Simulation of weakly self-similar stationary increment Sub_\phi(\Omega)-processes: a series expansion approach. Methodology and Computing in Applied Probability 7, 379-400.
  9. Sottinen, T. and Tudor, C.A. (2006) On the equivalence of multiparameter Gaussian processes. Journal of Theoretical Probability 19, no. 2., 461-485.
  10. Gasbarra, D., Sottinen, T. and Valkeila, E. (2007) Gaussian bridges. Stochastic Analysis and Applications. Volume 2 of the series Abel Symposia, pp. 361-382.
  11. Bender, C., Sottinen, T. and Valkeila, E. (2007) Arbitrage with fractional Brownian motion? Theory of Stochastic Processes 13 (29), 23-34.
  12. Sottinen, T. and Tudor, C.A. (2008) Parameter estimation for stochastic equations with additive fractional Brownian sheet. Statistical Inference for Stochastic Processes 11, 221-236.
  13. Särkkä, S. and Sottinen, T. (2008) Application of Girsanov Theorem to Particle Filtering of Discretely Observed Continuous-Time Non-Linear Systems. Bayesian Analysis 3, no. 3., 555-584.
  14. Bender, C., Sottinen, T. and Valkeila, E. (2008) Pricing by hedging and no-arbitrage beyond semimartingales. Finance and Stochastics 12, 441-468.
  15. Morlanes, J. I., Rasila, A. and Sottinen, T. (2009) Empirical evidence on arbitrage by changing the stock exchange. Advances and Applications in Statistics, no. 2, Vol. 12, 223-233.
  16. Kozachenko, Yu., Sottinen, T. and Vasylyk, O. (2011) Lipschitz conditions for Sub_\phi(\Omega)-processes with application to weakly self-similar stationary increment processes. Theory Probab. Math. Stat. 82, 57-73.
  17. Gapeev, P., Sottinen, T. and Valkeila, E. (2011) Robust replication in H-self-similar Gaussian market models under uncertainty. Statistics & Risk Modeling 28, 37-50.
  18. Gasbarra, D., Sottinen, T., and van Zanten, H. (2011) Conditional full support of Gaussian processes with stationary increments. Journal of Applied Probability 48, No. 2., 561-568.
  19. Bender, C., Sottinen, T. and Valkeila, E. (2011) Fractional procesess as models in stochastic finance. Advanced Mathematical Methods for Finance. Series in Mathematical Finance, Springer, pp.75-103.
  20. Sottinen, T. and Yazigi, A. (2014) Generalized Gaussian Bridges. Stochastic Processes and their Applications 124, Issue 9, 3084-3105.
  21. Azmoodeh, E., Sottinen, T., Viitasaari, L. and Yazigi, A. (2014) Necessary and Sufficient Conditions for Hölder Continuity of Gaussian Processes. Statistics & Probability Letters 94, 230-235.
  22. Azmoodeh, E., Sottinen, T. and Viitasaari, L. (2015) Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian-fractional Brownian model. Modern Stochastics: Theory and Applications, 2, No. 1, 29-49.
  23. Sottinen, T. and 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, No 3 (Proceedings of PRESTO-2015 conference), 287-295.
  24. Sottinen, T. and Viitasaari, L. (2016) Pathwise integrals and Ito-Tanaka Formula for Gaussian processes. Journal of Theoretical Probability 29, Issue 2, 590-616.
  25. Sottinen, T. and Viitasaari, L. (2016) Stochastic Analysis of Gaussian Processes via Fredholm Representation. International Journal of Stochastic Analysis, doi:10.1155/2016/8694365.
  26. Pakkanen, M.S., Sottinen, T. and Yazigi, A. (2017) On the conditional small ball property of multivariate Levy-driven moving average processes, Stochastic Processes and their Applications, 127, Issue 3, 749-782.
  27. Yang, X., Rasila, A. and Sottinen, T. (2017) Walk on Spheres Algorithm for Helmholtz and Yukawa Equations via Duffin Correspondence. Methodology and Computing in Applied Probability, 19, 589-602.
  28. Sottinen, T. and Viitasaari, L. (2017) Prediction Law of Fractional Brownian Motion. Statistics & Probability Letters 129, 155-166.
  29. Shokrollahi, F. and Sottinen, T. (2017) Hedging in fractional Black-Scholes model with transaction costs. Statistics & Probability Letters 130, 85-91.
  30. Sottinen, T. and Viitasaari, L. (2018) Conditional-Mean Hedging Under Transaction Costs in Gaussian Models. International Journal of Theoretical and Applied Finance 21, no. 2.
  31. Rasila, A. and Sottinen, T. (2018) Yukawa Potential, Panharmonic Measure and Brownian Motion. Axioms 2018, 7(2), 28.
  32. Sottinen, T. and Viitasaari, L. (2018) Parameter Estimation for the Langevin Equation with Stationary-Increment Gaussian Noise. Statistical Inference for Stochastic Processes 21 (3), 569-601.
  33. Sottinen, T. and Viitasaari, L. (2019) Transfer Principle for nth Order Fractional Brownian Motion with Applications to Prediction and Equivalence in Law. Theory of Probability and Mathematical Statistics 98, 199-216.
  34. Yang, X., Rasila, A. and Sottinen, T. (2019) Efficient simulation of Schrödinger equation with piecewise constant positive potential. Mathematics and Computers in Simulation 166, 315-323.
  35. Lehto, S., Ernvall-Hytönen, A.-M. and Sottinen, T. (2019) Divisible Skylines: Exploring Least Common Multiples and Divisibility through Visual Art. Bridges 2019 short paper.
  36. Sottinen, T. and Viitasaari, L. (2020) Prediction Law of Mixed Gaussian Volterra Processes. Statistics & Probability Letters 156, January 2020, 108594, https://doi.org/10.1016/j.spl.2019.108594
  37. Azmoodeh, E., Sottinen, T., Tudor, C.A. and Viitasaari, L. (2021) Integration-by-Parts Characterizations of Gaussian Processes. Collectanea Mathematica 72, 25-41.
  38. Sottinen, T., Alos, E., Azmoodeh, E. and Di Nunno, G. (2021) Editorial: Long-Memory Models in Mathematical Finance. Frontiers in Applied Mathematics and Statistics 7, 28.
  39. Merino, R., Pospisil, J., Sobotka, T., Sottinen, T. and Vives, J. (2021) Decomposition formula for rough Volterra stochastic volatility models. International Journal of Theoretical and Applied Finance 24, No. 02, 2150008 https://doi.org/10.1142/S0219024921500084
  40. Sottinen, T. (2021) The Characterization of Brownian Motion as an Isotopic i.i.d.-component Lévy Process. In Contributions to Mathematics and Statistics: Essays in Honor of Seppo Hassi (eds. De Snoo, H.S.V. and Wietsma, H.L.), Acta Wasaensia 462, 179-186.
  41. Dufitinema, J., Pynnönen, S. and Sottinen, T. (2022) Maximum likelihood estimators from discrete data modeled by mixed fractional Brownian motion with application to the Nordic stock markets. Communications in Statistics - Simulation and Computation. https://doi.org/10.1080/03610918.2020.1764581
  42. Sottinen, T. (2022) Brownian Bridges on Polygons. Proceedings of Bridges 2022: Mathematics, Art, Music, Architecture, Culture
  43. Maleki Almani, H. and Sottinen, T. (2023) Multi-mixed fractional Brownian motions and Ornstein-Uhlenbeck processes. Modern Stochastics: Theory and Applications, Vol 10, No. 4, 343-366. https://doi.org/10.15559/23-VMSTA229
  44. Azmoodeh, E., Ilmonen, P, Shafik, N., Sottinen, T. and Viitasaari, L. (2023) On Sharp Rate of Convergence for Discretization of Integrals Driven by Fractional Brownian Motions and Related Processes with Discontinuous Integrands. Journal of Theoretical Probability. https://doi.org/10.1007/s10959-023-01272-7
  45. Dufitinema, J., Shokrollahi, F., Sottinen, T. and Viitasaari, L. (2024) Long-range dependent completely correlated mixed fractional Brownian motion. Stochastic Processes and Their Applications, Volume 170, April 2024, 104289. https://doi.org/10.1016/j.spa.2023.104289
  46. Maleki Almani, H., Shokrollahi, F., and Sottinen, T. (2024) Prediction of Gaussian Volterra Processes with Compound Poisson Jumps. Statistics and Probability Letters, Volume 208, May 2024, 110054. https://doi.org/10.1016/j.spl.2024.110054
  47. Sottinen, T., Sönmez, E., and Viitasaari, L. (2024) On the existence and regularity of local times. Electron. J. Probab. 29 1-27, 2024. https://doi.org/10.1214/24-EJP1172
  48. Han, Q., Rasila, A. and Sottinen, T. (2025) Efficient simulation of mixed boundary value problems and conformal mappings. Applied Mathematics and Computation 488, 1 March 2025, 129119 https://doi.org/10.1016/j.amc.2024.129119

    Preprints

  49. Sottinen, T. and Valkeila, E. (2001) Fractional Brownian motion as a model in finance. University of Helsinki, Department of Mathematics, Preprint 302.
  50. Van Bever, G., Ilmonen, P., Viitasaari, L., Shafik, N. and Sottinen, T. (2022) On optimal prediction of missing functional data with memory. arXiv preprint arXiv:2208.09925
  51. Sottinen, T. and Viitasaari, L. (2023) Transfer principle for fractional Ornstein-Uhlenbeck processes. arXiv preprint arXiv:2311.00823
  52. Maleki Almani, H. and Sottinen, T. (2024) Parameter estimation for multi-mixed fractional Ornstein-Uhlenbeck processes by generalized method of moments. arXiv preprint arXiv:2401.05114
  53. Ralchenko, K., Shokrollahi, F. and Sottinen, T. (2024) Discretization of integrals driven by multifractional Brownian motions with discontinuous integrands arXiv preprint arXiv:2408.02449
  54. Maleki Almani, H., Shokrolahi, F. and Sottinen, T. (2024) Hedging in Jump Diffusion Model with Transaction Costs arXiv preprint arXiv:2408.10785

    Other publications (most in Finnish)

  55. Sottinen, T. (2004) Nobelin muistopalkinto taloustieteestä 2003: R. Englen ARCH-malli. Arkhimedes 2004:2, 10-12 (in Finnish).
  56. Sottinen, T. (2004) Sattuman matematiikkaa III: Kolmogorovin aksioomat ja frekvenssitulkinta. Solmu 2004:2, 17-21 (in Finnish).
  57. Lehto, S. and Sottinen, T. (2005) Sisarusongelma - paradoksi ehdollisesta todennäköisyydestä. Solmu 2005:1, 14-15 (in Finnish).
  58. Rasila, A., and Sottinen, T. (2005) Algebra, PlayStation ja älykkyys. Solmu Erikoisnumero 1/2005-2006 (in Finnish).
  59. Norros, I. and Sottinen, T. (2013) Esko Valkeila 1951-2012. Arkhimedes 2013:1, 30-33 (in Finnish).
  60. Sottinen, T. (2015) BS-kaava ja lama. Arkhimedes 2015:1, 26-30 (in Finnish).
  61. Sottinen, T. (2016) Moni sekoaa muotiin. Professoriblogi 2.5.2016.
  62. Sottinen, T. (2016) Häränpaskahommia. Professoriblogi 12.9.2016.
  63. Sottinen, T. (2016) Muotia maailmalla. Professoriblogi 28.11.2016.
  64. Sottinen, T. (2017) Yliopistojen autonomia ja universumin maksimaalisen ironian periaate. Professoriblogi 27.2.2017.
  65. Sottinen, T. (2017) Avoin tiede. Professoriblogi 29.5.2017.

    Lecture notes (some in Finnish)

  66. Malliavin-laskenta: Eli gaussisten prosessien derivointi., 87 pages, 2006.
  67. Rahoitusteoria: Eli optioiden hinnoittelun ja toistamisen taito tai oppi optioiden oikeasta hinnasta., 149 pages, 2006.
  68. Todennäköisyysteoria: Teoria mitasta, mitallisuudesta, mitattomuudesta ja riippumattomuudesta., 130 pages, 2006.
  69. Operations Research with GNU Linear Programming Kit, 201 pages, 2009.
  70. Päätöksenteko epävarmuuden vallitessa, 102 pages, 2010.
  71. Operations Research with GNU Octave, 187 pages, 2011.
  72. Päätöksiä ja Paatoksia, 146 pages, 2011.
  73. Probability and Stochastic Processes with a Twist of GNU Octave towards Queuing, 183 pages, 2019.
  74. Lineaarialgebraa lähinnä tasossa hipauksella GNU Octavea, 81 pages, 2022.
  75. Octave with Spice: Or a Gentle Introduction to GNU Octave Towards Linear Programming, 38 pages, 2022.
  76. Linear Programming with Spice: Or a Gentle Introduction to Linear Models, 73 pages, 2022.
  77. Päätöksentekoa Oliopolion aikaan, 86 pages, 2023.
  78. A Gentle Introduction to Stochatic Differential Equations with Brownian noise, 28 pages, 2023.

List of publications from AMS Mathematical Reviews, Zentralblatt MATH, and Google Scholar.

Collaborators

  1. Elisa Alòs, Pompeu Fabra University, Spain
  2. Ehsan Azmoodeh, Univerity of Liverpool, UK
  3. Christian Bender, Saarland University, Germany
  4. Germain Van Bever, University of Namur, Belgium
  5. Josephine Dufitinema, IQVIA, Finland
  6. Anne-Maria Ernvall-Hytönen, University of Helsinki, Finland
  7. Pavel Gapeev, London School of Economics, UK
  8. Dario Gasbarra, University of Helsinki, Finland
  9. Hagen Gilsing
  10. Qiansheng Han, Guangdong Technion - Israel Institute of Technology, PRC
  11. Pauliina Ilmonen, Aalto University, Finland
  12. Yuriy Kozachenko
  13. Hamidreza Maleki Almani, University of Vaasa, Finland
  14. Raúl Merino, University of Barcelona, Spain
  15. Igor Morlanes, Stockholm University, Sweden
  16. Giulia Di Nunno, University of Oslo, Norway
  17. Mikko S. Pakkanen, Imperial College London, UK
  18. Jan Pospíšil, University of West Bohemia, Czechia
  19. Seppo Pynnönen, University of Vaasa, Finland
  20. Antti Rasila, Guangdong Technion - Israel Institute of Technology, PRC
  21. Simo Särkkä, Aalto University, Finland
  22. Nourhan Shafik, Aalto University, Finland
  23. Foad Shokrollahi, University of Vaasa, Finland
  24. Tomáš Sobotka, University of West Bohemia, Czechia
  25. Ercan Sönmez, University of Klagenfurt, Austria
  26. Ciprian A. Tudor, University of Lille 1, France
  27. Esko Valkeila
  28. Olga Vasylyk, Taras Shevchenko Kyiv National University, Ukraine
  29. Lauri Viitasaari, Aalto University, Finland
  30. Xuxin Yang, Hunan First Normal University, PRC
  31. Josep Vives, University of Barcelona, Spain
  32. Adil Yazigi, University of Eastern Finland, Finland
  33. Harry van Zanten, University of Amsterdam, The Netherlands

Talks

  1. Fractional Brownian motion, random walks, and binary market models, The 2nd Nordic-Russian Symposium on Stochastic Analysis, Beitostølen, Norway, 1-6 August 1999.
  2. Fractional Brownian Motion as a Model in Finance, Analysis of High Frequency Data: Annual Meeting of the Finnish Statistical Society, Vaasa, Finland, 17-18 May 2001.
  3. Sample path large deviations of a Gaussian process with stationary increments and regularly varying variance, 12th European Young Statisticians Meeting, Janska Dolina, Slovakia, 4-8 September 2001.
  4. Busy periods of a fractional Brownian type Gaussian storage, A conference dedicated to the 90th anniversary of B. V. Gnedenko, Kyiv, Ukraine, 3-7 June 2002.
  5. On Gaussian stochastic differential equations with fractional Brownian noise, Laugarvatn Workshop: Stochastic Analysis and its Applications, Laugarvatn, Iceland, 2-7 August 2002.
  6. Arbitrage in the fractional Black-Scholes model, Seminar in Mathematical Statistics, University of Stockholm, Stockholm, Sweden, 16 January 2003.
  7. Power series series expansions of fractional Brownian motion, The Seventh International School on Mathematical and Statistical Methods in Economics, Finance and Insurance, Laspi, Ukraine, September 2003. (Invited)
  8. Gaussian bridges, Groupe de travail: Processus Stochastiques, Matrices Aléatoires, University of Paris VI, Paris, France, 15 January 2004.
  9. Representations of Gaussian bridges, DYNSTOCH Workshop, Copenhagen, Denmark, 3-5 June 2004.
  10. Fractional Brownian Motions and Sheets, Porkkala Fractional Symposium, Porkkala, Finland, 25 May 2005.
  11. Gaussian Bridges, 35th International Probability Summer School, Saint-Flour, France, 6-23 July 2005.
  12. Replication and Absence of Arbitrage in Non-Semimartingale Models, The Finnish Mathematical Days and the Second Finnish-Estonian Mathematical Colloquium, Tampere, Finland, 4-5 January 2006.
  13. Replication and Absence of Arbitrage in Non-Semimartingale Models, Probability Seminar, University of Barcelona, Barcelona, Spain, 15 March 2006.
  14. Are stylized facts irrelevant in option-pricing? International Conference Modern Stochastics: Theory and Applications, Kyiv, Ukraine, 19-23 June 2006.
  15. On Skorohod-type stochastic differential equations with respect to fractional Brownian motion, 31st Conference on Stochastic Processes and their Applications, Paris, France, 17-21 July 2006. (Invited)
  16. Black-Scholes Prices with Stylized Facts, Russian-Scandinavian Symposium: Probability Theory and Applied Probability, Petrozavodsk, Russia, 26-31 August 2006.
  17. Black-Scholes-hinnoittelumallin robustisuus ja tyylitellyt tosiseikat, Monthly meeting of the Actuarial Society of Finland, 10 October 2006.
  18. Conditional Small Balls and No-Arbitrage, Advances in Mathematical Finance, Second General AMAMEF Conference and Banach Center Conference, Bedlewo, Poland, 30 April-5 May 2007. (Invited)
  19. What is the Price of the Future?, The Icelandic Centre of Excellence in Theoretical Computer Science ICE-TCS Third Symposium on Theoretical Computer Science, Reykjavik, Iceland, 10 August 2007.
  20. Local Continuity Of Stopping Times And Arbitrage, Workshop and Mid-Term Conference on Advanced Mathematical Methods for Finance, Vienna, Austria, 17-22 September 2007.
  21. Local Continuity, Mathematics Seminar, University of Iceland, Iceland, 25 October 2007.
  22. Probability is irrelevant in stochastic finance: Black-Scholes model is correct despite of stylized facts, Annual meeting of the Icelandic Mathematical Society, Borgarnes, Iceland, 29-30 November 2007. (Invited)
  23. Local Continuity (for Stopping Times), the Finnish Mathematical Days, Espoo, Finland, 3-4 January 2008. (Invited)
  24. Local Continuity, Workshop on Limit theorems and Applications, Paris, France, 14-16 January 2008. (Invited)
  25. What is Volatility?, The 6th NoonToNoon Meeting: Insurance and Financial Mathematics - Theory and Practice, Jyväskylä, Finland, 2-3 October 2008.
  26. Non-semimartingales in finance, 1st Northern Triangular Seminar, Espoo, Finland, 9-11 March 2009. (Tutorial)
  27. On Conditional Full Support with Applications to Mathematical Finance, 25th Nordic and 1st British-Nordic congress of Mathematicians, Oslo, Norway, 8-11 June 2009. (Invited)
  28. Conditional full support for Gaussian processes with stationary increments, Modern Stochastics: Theory and Applications II, Kyiv, Ukraine, 7-11 September 2010. (Invited)
  29. "Todellinen" veroprosentti: Kaksi ajankohtaista esimerkkiä talousmatematiikasta ja "todellisuudesta", MAOL ry:n syyspäivät, Vantaa, Finland, 8-10 October 2010. (Invited)
  30. Pricing by hedging and no-arbitrage beyond semimartingales, International symposium: Visions in stochastics (Leaders and their Pupils), Moscow, Russia, 1-3 November 2010.
  31. No-Arbitrage with Non-Semimartingales: Continuous Simple Arbitrage Case, Seventh Seminar on Stochastic Analysis, Random Fields and Applications, Ascona, Switzerland, 23-27 May 2011.
  32. Black ja Scholes ilman Gaussia, Annual meeting of the Finnish Mathematical Society, Helsinki, Finland, 19 March 2012. (Invited)
  33. Generalized Gaussian Bridges of Prediction-Invertible Processes, Presentation at Hunan Normal University, Changsha, China, 22 May 2012.
  34. Black-Scholes Prices and Hedges for Financial Derivatives in Non-Gaussian Non-Martingale Models, International Conference on Applied Mathematics 2012, Modeling, Analysis & Computation, City University of Hong Kong, Hong Kong, China, 30 May 2012.
  35. Yukawa Potential, Harmonic Measure and Killing Brownian Motion, First Chinese-Finnish Seminar and Workshop on Modern Trends in Classical Analysis and Applications, Turku, Finland, 18 August 2012.
  36. Generalized Gaussian Bridges of Prediction-Invertible Processes, Modern Stochastics: Theory and Applications III, Kyiv, Ukraine, 10 September 2012. (Invited)
  37. Generalized Gaussian Bridges, Marrakesh International Conference on Probability and Statistics, Marrakesh, Morocco, 19 December 2013. (Plenary)
  38. Necessary and Sufficient Conditions for Hölder Continuity of Gaussian Processes, Thiele Seminar, Aarhus University, Århus, Denmark, 26 March 2014.
  39. Necessary and Sufficient Conditions for Hölder Continuity of Gaussian Processes, ICM 2014, Seoul, Republic of Korea, 19 August 2014.
  40. Representing Gaussian Processes with Martingales with Application to MLE of Langevin Equation, Stochastic Visit Workshop of the FDPSS, Tartu, Estonia, 12 September 2014.
  41. Gaussian Fredholm Processes, International Conference: Probability, Reliability and Stochastic Optimization, Kyiv, Ukraine, 8 April 2015. (Plenary)
  42. Matematiikan täsmäopetuksella parempia insinöörejä, Interaktiivinen tekniikka koulutuksessa, ITK2015, Hämeenlinna, 17 April 2015.
  43. Gaussian Fredholm Processes with Applications, Yu.V.Linnik Centennial Conference, Euler International Mathematical Institute, St. Petersburg, Russia, 16 September 2015.
  44. Representing Gaussian Processes via Brownian Motion with Applications to Stochastic Analysis, talk at South Central University, Changsha, PRC, 30 October 2015.
  45. A Celebration of Dynkin's Formula, tutorial at Hunan First Normal University, Changsha, PRC, 26 November 2015.
  46. Walk On Spheres Algorithms for Helmholtz and Linearized Poisson-Boltzmann Equations, The Fifth Chinese-Finnish Seminar and Workshop on Modern Trends in Classical Analysis and Applications, Aalto University, Espoo, Finland, 9 February 2016.
  47. Parameter Estimation for the Langevin Equation with Stationary-Increment Gaussian Noise, Lorentz Center Workshop Fractatility and Fractionality, University of Leiden, Leiden, The Netherlands, 19 May 2016. (Invited)
  48. Gaussian (Fredholm) Processes, 37th Finnish Summer School on Stochastics and Statistics, Lammi, Finland, 30 May 2016.
  49. Hedging under transaction costs in Gaussian models, Barcelona Workshop on Mathematical Finance, Barcelona, Spain, 29 March 2017.
  50. Transfer Principle for nth-Order Fractional Brownian Motion with Applications to Prediction and Equivalence in Law, Modern Stochastics: Theory and Applications IV, Kyiv, Ukraine, 25 May 2018. (Plenary)
  51. Prediction law of fractional Brownian motion, ICM 2018, Rio de Janeiro, Brazil, 6 August 2018.
  52. Pretty Predictable Models, CMStatistics, London, UK, 15 December 2019. (Invited)
  53. Integration-by-Parts Characterizations of Gaussian Processes, Finnish Mathematical Days, Oulu, Finland, 2 January 2020.
  54. Option-Pricing without Probability: Good News and Bad News, IFAM Virtual Seminar, Liverpool, UK, 9 September 2020.
  55. Integration-by-Parts Characterizations of Gaussian Processes, Modern Trends in Probability Theory and Mathematical Statistics III, Kyiv, Ukraine, 1 December 2020. (Invited)
  56. Long-Range Dependent Completely Correlated Mixed Fractional Brownian motion, Modern Stochastics: Theory and Applications V, Kyiv, Ukraine, 4 June 2021. (Plenary)
  57. Integration-by-Parts Characterizations of Gaussian Processes, 8ECM, Portorož, Slovenia, 22 June 2021. (Invited)
  58. Conditional-mean hedging in Gaussian long-memory models with transaction costs, 10th General AMaMeF Conference, Padua, Italy, 25 June 2021. (Invited)
  59. Finanssijohdannaisten gaussiset hinnat ja keskeisen raja-arvolauseen väärinymmärrys, MAL 60 vuotta juhlaseminaari, Helsinki, Finland, 12 November 2021. (Invited)
  60. A New characterization of Brownian motion as isotropic i.i.d.-component Lévy process, Finnish Mathematical Days, Tampere, Finland, 4 January 2022.
  61. Completely correlated mixed fractional Brownian motion, Stochastic processes with statistical applications and fractional stochastic calculus: International workshop dedicated to the anniversary of Yuliya Mishura, Kyiv, Ukraine (online), 17 May 2023. (Invited)
  62. Completely correlated mixed fractional Brownian motion, Mathematical Finance and Stochastics: A Conference in Honor of David Nualart, Donostia, Spain, 31 May 2023. (Invited)
  63. Integration-by-parts characterizations of Gaussian processes, Workshop on Stochastics, Memory and Roughness 2024, Oslo, Norway, 18 January 2024. (Invited)

Ph.D. students

  1. Dr. Mikko S. Pakkanen (University of Helsinki, 2010)
  2. Dr. Lauri Viitasaari (Aalto University, 2014)
  3. Dr. Adil Yazigi (University of Vaasa, 2015)
  4. Dr. Foad Shokrollahi (University of Vaasa, 2019)