"Talousmatematiikka" - Selaus asiasanan mukaanArtikkelit

    • Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian–fractional Brownian model 

      Azmoodeh, Ehsan; Sottinen, Tommi; Viitasaari, Lauri (VTeX, 11.05.2015)
      We study asymptotic normality of the randomized periodogram estimator of quadratic variation in the mixed Brownian–fractional Brownian model. In the semimartingale case, that is, where the Hurst parameter H of the fractional ...
    • Fredholm representation of multi-parameter Gaussian processes with applications to equivalence in law and series expansions 

      Sottinen, Tommi; Viitasaari, Lauri (VTeX, 2015)
      We show that every multiparameter Gaussian process with integrable variance function admits a Wiener integral representation of Fredholm type with respect to the Brownian sheet. The Fredholm kernel in the ...
    • Generalization of the Nualart–Peccati criterion 

      Azmoodeh, Ehsan; Malicet, Dominique; Mijoule, Guillaume; Poly, Guillaume (Institute of Mathematical Statistics, 14.03.2016)
      The celebrated Nualart–Peccati criterion [Ann. Probab. 33 (2005) 177–193] ensures the convergence in distribution toward a standard Gaussian random variable N of a given sequence {Xn}n≥1 of multiple Wiener–Itô integrals ...
    • Generalized Gaussian bridges 

      Sottinen, Tommi; Yazigi, Adil (ElsevierNorth-Holland Publ. Co.Bernoulli Society for Mathematical Statistics and Probability, 2014)
      A generalized bridge is a stochastic process that is conditioned on N linear functionals of its path. We consider two types of representations: orthogonal and canonical. The orthogonal representation is constructed from ...
    • On the conditional small ball property of multivariate Lévy-driven moving average processes 

      Pakkanen, Mikko S.; Sottinen, Tommi; Yazigi, Adil (Elsevier, 01.03.2017)
      We study whether a multivariate Lévy-driven moving average process can shadow arbitrarily closely any continuous path, starting from the present value of the process, with positive conditional probability, which we call ...
    • Parameter estimation for the Langevin equation with stationary-increment Gaussian noise 

      Sottinen, Tommi; Viitasaari, Lauri (Springer, 24.01.2017)
      We study the Langevin equation with stationary-increment Gaussian noise. We show the strong consistency and the asymptotic normality with Berry–Esseen bound of the so-called second moment estimator of the mean reversion ...
    • Prediction law of fractional Brownian motion 

      Sottinen, Tommi; Viitasaari, Lauri (Elsevier, 01.10.2017)
      We calculate the regular conditional future law of the fractional Brownian motion with index H ∈(0, 1) conditioned on its past. We show that the conditional law is continuous with respect to the conditioning path. We ...