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Decomposition formula for rough Volterra stochastic volatility models
(World Scientific Publishing Company, 2021-04-14)
- article
The research presented in this paper provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners ...
Brownian Bridges on Polygons
(Tessellations Publishing, 2022)
- article
There are no straight lines or sharp corners in nature, said the famous Catalan architect Antoni Gaudí. The famous Polish–French–American mathematician Benoit B. Mandelbrot went even further and asserted that the curves ...
Divisible skylines : exploring least common multiples and divisibility through visual art
(Tessellations Publishing, 2019)
- conferenceObject
We present an alternative way to consider number theoretic concepts through visual art. Our visualization method, Divisible Skylines, is an artistically motivated study of least common multiples. It demonstrates how beauty ...
Generalized Gaussian bridges
(ElsevierNorth-Holland Publ. Co.Bernoulli Society for Mathematical Statistics and Probability, 2014)
- article
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 ...
Fredholm representation of multi-parameter Gaussian processes with applications to equivalence in law and series expansions
(VTeX, 2015)
- article
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 ...
Conditional-mean hedging under transaction costs in Gaussian models
(World Scientific Publishing Company, 2018-04-02)
- article
We consider so-called regular invertible Gaussian Volterra processes and derive a formula for their prediction laws. Examples of such processes include the fractional Brownian motions and the mixed fractional Brownian ...
On the conditional small ball property of multivariate Lévy-driven moving average processes
(Elsevier, 2017-03-01)
- article
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
(Springer, 2017-01-24)
- article
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 ...
Transfer Principle for nth order Fractional Brownian Motion with Applications to Prediction and Equivalence in Law
(2018)
- article
The n-th order fractional Brownian motion was introduced by Perrin et al. [13]. It is the (up to a multiplicative constant) unique self-similar Gaussian process with the Hurst index H∈(n-1,n), having n-th order stationary ...
Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian–fractional Brownian model
(VTeX, 2015-05-11)
- article
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 ...