Results 71 to 80 of about 243,967 (218)

Identification of the Multivariate Fractional Brownian Motion [PDF]

IEEE Transactions on Signal Processing, 2011
This paper deals with the identification of the multivariate fractional Brownian motion, a recently developed extension of the fractional Brownian motion to the multivariate case. This process is a $p$-multivariate self-similar Gaussian process parameterized by $p$ different Hurst exponents $H_i$, $p$ scaling coefficients $ _i$ (of each component) and
Amblard, Pierre-Olivier, Coeurjolly, Jean-François   +1 more
openaire   +5 more sources

Parametric Estimation for Processes Driven by Infinite Dimensional Mixed Fractional Brownian Motion [PDF]

arXiv, 2021
Parametric and nonparametric inference for stochastic processes driven by a fractional Brownian motion were investigated in Mishura (2008) and Prakasa Rao(2010) among others. Similar problems for processes driven by an infinite dimensional fractional Brownian motion were studied in Prakasa Rao (2004,2013), Cialenco (2009) and others.
arxiv  

Lacunary Fractional Brownian Motion [PDF]

ESAIM: Probability and Statistics, 2012
In this paper, a new class of Gaussian field is introduced called Lacunary Fractional Brownian Motion. Surprisingly we show that usually their tangent fields are not unique at every point. We also investigate the smoothness of the sample paths of Lacunary Fractional Brownian Motion using wavelet analysis.
openaire   +3 more sources

Wasserstein Convergence for Empirical Measures of Subordinated Fractional Brownian Motions on the Flat Torus [PDF]

arXiv, 2023
We estimate rates of convergence for empirical measures associated with the subordinated fractional Brownian motion to the uniform distribution on the flat torus under the Wasserstein distance $\mathbb{W}_p$ for all $p\geq1$. In particular, our results coincides with recent ones on the diffusion process and the fractional Brownian motion.
arxiv  

Small values and functional laws of the iterated logarithm for operator fractional Brownian motion

Open Mathematics
The multivariate Gaussian random fields with matrix-based scaling laws are widely used for inference in statistics and many applied areas. In such contexts, interests are often Hölder regularities of spatial surfaces in any given direction.
Wang Wensheng, Dong Jingshuang
doaj   +1 more source

Sample Paths Estimates for Stochastic Fast-Slow Systems Driven by Fractional Brownian Motion [PDF]

Journal of statistical physics, 2019
We analyze the effect of additive fractional noise with Hurst parameter $$H > {1}/{2}$$ H > 1 / 2 on fast-slow systems. Our strategy is based on sample paths estimates, similar to the approach by Berglund and Gentz in the Brownian motion case.
Katharina Eichinger, C. Kuehn, Alexandra Neamţu   +2 more
semanticscholar   +1 more source

Spectral content of fractional Brownian motion with stochastic reset [PDF]

Journal of Physics A: Mathematical and Theoretical, 2018
We analyse the power spectral density (PSD) ST(f) (with T being the observation time and  f  the frequency) of a fractional Brownian motion (fBm), with an arbitrary Hurst index , undergoing a stochastic resetting to the origin at a constant rate r—the ...
S. Majumdar, G. Oshanin
semanticscholar   +1 more source

The fractional mixed fractional brownian motion and fractional brownian sheet [PDF]

ESAIM: Probability and Statistics, 2007
We introduce the fractional mixed fractional Brownian motion and fractional Brownian sheet, and investigate the small ball behavior of its sup-norm statistic. Then, we state general conditions and characterize the sufficiency part of the lower classes of some statistics of the above process by an integral test.
openaire   +1 more source

Cylindrical Fractional Brownian Motion in Banach Spaces [PDF]

Stochastic Process. Appl. 124 (2014), no. 11, pp 3507-3534, 2013
In this article we introduce cylindrical fractional Brownian motions in Banach spaces and develop the related stochastic integration theory. Here a cylindrical fractional Brownian motion is understood in the classical framework of cylindrical random variables and cylindrical measures.
arxiv   +1 more source

Large deviation for slow-fast McKean-Vlasov stochastic differential equations driven by fractional Brownian motions and Brownian motions [PDF]

arXiv, 2023
In this article, we consider slow-fast McKean-Vlasov stochastic differential equations driven by Brownian motions and fractional Brownian motions. We give a definition of the large deviation principle (LDP) on the product space related to Brownian motion and fractional Brownian motion, which is different from the traditional definition for LDP.
arxiv