Fakultäten der RUB » Fakultät für Mathematik » Lehrstühle » Arbeitsgruppe Stochastik/Didaktik

Research Interests

  • Probabilistic limit theorems
  • Stochastic analysis on Wiener spaces
  • Gaussian analysis
  • Poisson analysis
  • Malliavin calculus
  • Stein's method
  • Statistical inferences of stochastic processes
  • Mathematical finance
  • Fractional Brownian motion


  • 1. Azmoodeh, E., Mishura, Y., Valkeila, E. (2009). On hedging European options in geometric fractional Brownian motion market model, Statistics & Decisions, Vol. 27, 129-143.
  • 2. Azmoodeh, E., Tikanmäki, H., Valkeila, E. (2010). When does fractional Brownian motion not behave as a continuous function with bounded variation?, Statistics & Probability Letters, Vol 80, Issues 19-20, 1543-1550.
  • 3. Azmoodeh, E., Valkeila, E. (2013). Spectral characterization for the quadratic variation of mixed Brownian fractional Brownian motion, Stat. Inference Stoch. Process. 16, no. 2, 97-112.
  • 4. Azmoodeh, E. (2013). On the fractional Black-Scholes market with transaction costs. Communications in Mathematical Finance, Vol. 2, no.3, 21-40.
  • 5. Azmoodeh, E., Viitasaari, L. (2013). Rate of convergence and discretization of stochastic integrals with respect to fractional Brownian motion. Journal of Theoretical Probability. Vol. 28, Issue 1, 396-422.
  • 6. Azmoodeh, E., Morlanes, I. (2013). Drift parameter estimation for fractional Ornstein-Uhlenbeck process of the Second Kind. Statistics: A Journal of Theoretical and Applied Statistics. Vol. 49, Issue 1, 1-18.
  • 7. Azmoodeh, E., Campese, S., Poly, G. (2014). Fourth Moment Theorems for Markov Diffusion Generators. Journal of Functional Analysis, Vol. 266, no. 4, 2341–2359.
  • 8. Azmoodeh, E., Sottinen, T., Viitasaari, L., Yazigi, A. (2014). Necessary and Sufficient Conditions for Hölder Continuity of Gaussian Processes. Statistics & Probability Letters, Vol 94, 230-235.
  • 9. Azmoodeh, E., Viitasaari, L. (2014). A general approach to small deviation via concentration of measures. Arxiv
  • 10. Azmoodeh, E., Viitasaari, L. (2015). Parameter estimation based on discrete observations of fractional Ornstein-Uhlenbeck process of the second kind. Stat. Inference Stoch. Process. Vol. 18, Issue 3, 205-227. Arxiv
  • 11. 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. Vol. 2 , No. 1, 29-49. Arxiv
  • 12. Azmoodeh, E., Peccati, G., Poly, G. (2015). Convergence towards linear combinations of chi-squared random variables: a Malliavin-based approach. Séminaire de Probabilités (Special volume in memory of Marc Yor) 339-367. Arxiv
  • 13. Azmoodeh, E., Peccati, G. (2015). Optimal Berry-Esseen bounds on the Poisson space. Arxiv
  • 14. Azmoodeh, E., Malicet, D., Mijoule, G., Poly, G. (2016). Generalization of the Nualart-Peccati criterion. The Annals of Probability. Vol. 44, No. 2, 924-954. Arxiv
  • 15. Azmoodeh, E., Peccati, G., Poly, G. (2016). The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds. To appear in ALEA. Arxiv
  • 16. Arras, B., Azmoodeh, E., Poly, G., Swan, Y. (2017). A bound on the 2-Wasserstein distance between linear combinations of independent random variables. To appear in Stochastic processes and their applications. Arxiv
  • 17. Azmoodeh, E., Gasbarra, D. (2017). New moments criteria for convergence towards normal product/tetilla laws. Arxiv
  • 18. Arras, B., Azmoodeh, E., Poly, G., Swan, Y. (2017). Stein characterizations for linear combinations of gamma random variables. To appear in Brazilian Journal of Probability and Statistics. Arxiv
  • 19. Azmoodeh, E., Gasbarra, D. (2018). On a new Sheffer class of polynomials related to normal product distribution. To appear in Theory of Probability and Mathematical Statistics. Arxiv
  • 20. Azmoodeh, E., Eichelsbacher, P., Knichel, L. (2018). On the Rate of Convergence to a Gamma Distribution on Wiener Space. Arxiv
  • 21. Azmoodeh, E., Nourdin, I. (2018). Almost sure limit theorems on Wiener chaos: the non-central case. Arxiv
  • 22. Azmoodeh, E., Peccati, G. (2018). Malliavin-Stein Method: a Survey of Recent Developments. Arxiv

  • PhD Thesis (Aalto University, 2010): Riemann-Stieltjes Integrals with Respect to Fractional Brownian Motion and Applications.
  • Master Thesis (Sharif University of Technology, 2005): Stochastic Calculus with Respect to Fractional Brownian Motion and its Application in Mathematical Finance.


  • 2007
    1. The 29th Finnish Summer School on Probability Theory, In Nagu/Nauvo, 4-8 June, 2007
    2. 5th International Conference on Levy Processes: Theory and Applications and Satellite Sum- mer School, Copenhagen, 13-17 August 2007 and Sandbjerg 9-12 August 2007

  • 2008
    3. An estimator for the quadratic variation of mixed Brownian fractional Brownian motion, Aalto Stochastics Seminar, Spring 2008
    4. The 30th Finnish Summer School on Probability Theory, Tampere, 2-6 June, 2008
    5. An estimator of the quadratic variation of a process with nite energy, In European Summer School in Financial Mathematics, Paris 7-14 September 2008

  • 2009
    6. On hedging problem of a path-dependent option in fractional Black-Scholes market, Aalto Stochastics Seminar
    7. On hedging European options in fractional market, 1st Northern Triangular Seminar, Espoo 9-11 March 2009, Helsinki University of Technology
    8. On hedging of European options in fractional Black-Scholes model, Fourth General Conference on Advances Mathematical Methods in Finance, Alesund 4-10 May 2009
    9. European call option and fractional frictionless/friction Market, Non-Semimartingale Techniques in Mathematical Finance, Espoo 26-28,May 2009, Helsinki University of Technology

  • 2010
    10. 2nd Northern Triangular Seminar, Stockholm 15-17 March 2010, Royal Institute of Technology (KTH)
    11. Riemann-Stieltjes integrals and applications in mathematical nance, The 32nd Finnish Summer School on Probability Theory, Tampere 7-11 June 2010
    12. Approximate hedging of contingent claims under transaction costs in GFBM, International Symposium, Visions in Stochastics, Moscow 1-4 November 2010, Steklov Mathematical Institute

  • 2011
    13. On a non-semimartingale market with transaction costs, Seventh Seminar on Stochastic Analysis, Random Fields and Applications, Ascona, Switzerland, 23-27 May 2011, Poster session
    14. The 35th Conference on Stochastic Processes and their Applications, Oaxaca, Mexico 19-24 June 2011

  • 2012
    15. Parameter estimation in a fractional Ornstein-Uhlenbeck model, Stochastic Sauna Seminar, on wednesday 19.12.2012, University of Helsinki

  • 2013
    16. Parameter estimation in a fractional Ornstein-Uhlenbeck model, PL2US Workshop,
    February 21-22, 2013, Universitt des Saarlandes, Germany 17. New look to fourth moment theorem. Aalto Stochastics Seminar, Aalto University
    18. Stein's method and the law of the iterated logarithm, Noon-to-Noon Sauna Seminar of the FDPSS, December 12-13 2013, University of Helsinki

  • 2014
    19. Generalization of the Nualart-Peccati criterion, NORDSTAT2014, 2-6 June, Turku, Finland
    20. Generalization of the Nualart-Peccati criterion, 11th International Vilnius Conference on Probability Theory and Mathematical Statistics, 30 June - 4 July, 2014, Vilnius, Lithuania
    21. How many cumulants are needed for convergence towards N1× N2 ?, Helsinki Stochastics Sauna Seminar, December 2014, Helsinki University, Finland.

  • 2015
    22. Convergence towards elements in the second Wiener chaos: a Malliavin-based approach, International Conference in Probability, Reliability and Stochastic Optimization, Kyiv, Ukraine, April 7-10, 2015
    23. Inference of realized volatility in fractional market models, 7th General AMaMeF conference, Advanced Mathematical Methods in Finance, (EPFL) Lausanne, Switzerland, September 7-10, 2015, Invited speaker in the Long--memory models section.
    24. Optimal Berry--Esseen bounds on the Poisson space, STOKASTISTEN MALLIEN SEMINAARI, Thursday, 22.10. 2015, Helsinki, Finland.

  • 2016
    25. On the optimality of Malliavin-Stein bound for normal approximation on the Poisson space, 12th German Probability and Statistics Days, 1 - 4 March, 2016, Bochum, Germany.
    26. Fourth moment theorems: revisit, generalization, applications and open problems, Oberseminar zur Stochastik, 31 March, 2016, Otto-von-Guericke-Universität Magdeburg, Germany.
    27. Stein's method on the second Wiener chaos, Fractality and Fractionality, 17-20 May 2016, Lorentz Center, Leiden, The Netherlands.
    28. An attempt to small deviations. Invited speaker at RTG Research Seminar, Monday, 20 June 2016, Essen, Germany.
    29. Convergence towards the second Wiener chaos. Stochastic seminar at Technische Universität Dortmund, Thursday, 10 November, Dortmund, Germany.

  • 2017
    30. The Malliavin--Stein method on the second Wiener chaos. Workshop on Fractional Brownian Motion and Rough Models, June 8-9, Balcelona, Spain.
    31. The Malliavin--Stein approach in probabilistic approximations. The 5th annual conference of Frontiers in Mathematical Sciences, 11-13 July, Tehran, IPM.
    32. Higher moment phenomenon for normal product/tetilla law. Summer school on probability and mathematical physics (X), September, Ghiffa, Italy.
  • Teaching

  • Ruhr University Bochum, Germany
    Teaching, Limit Theorems in Probability: modern view during summer 2017. Lecture note
    Teaching, Brownian motion during winter term 2017.
    Teaching Assistant, Analysis II during summer term 2018.
    Teaching, Introduction to Mathematical Finance during winter term 2018.
  • University of Helsinki
    Teaching, Probabilistic Approximations during spring 2015.
  • (Under)Graduate courses at Aalto University
    Teaching Assistant, Mat-1.3602 Stochastic Analysis during 2008-9 / III-IV.
    Teaching Assistant, Mat-1.3604 Stationary Processes during 2010-11/I-II.
    Teaching, Mat-1.9902 Fractional Brownian Motion during 2009-10/IV.
    Teaching, Mat-1.3601 Introduction to Stochastic during 2010-11/III-IV.
    Teaching, Mat-1.1610 Mathematics 1 during 2010-11/I-II.
    Teaching, Mat-1.2600 Applied Probability during 2008-9/I-II.
  • (Under)Graduate courses at University of Vaasa
    Teaching, Operation Research during Fall 2015.
    Teaching, Numerical Analysis during Fall 2015.
    Teaching, Probability and Stochastic Processes, Spring 2016.
  • Adresse

    Ruhr-Universität Bochum
    Gebäude IB 2/101
    Universitätsstraße 150
    44801 Bochum