An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process. [PDF]
Probab Theory Relat Fields, 2023 Assaf E, Buckley J, Feldheim N.
europepmc +1 more source
The Multiparameter Fractional Brownian Motion
, 2006 We define and study the multiparameter fractional Brownian motion. This process is a generalization of both the classical fractional Brownian motion and the multiparameter Brownian motion, when the condition of independence is relaxed. Relations with the
Herbin, Erick, Merzbach, Ely
core +1 more source
A random walk approximation to fractional Brownian motion [PDF]
arXiv, 2007 We present a random walk approximation to fractional Brownian motion where the increments of the fractional random walk are defined as a weighted sum of the past increments of a Bernoulli random walk.
arxiv
Log-Level Comparison Principle for Small Ball Probabilities [PDF]
arXiv, 2008 We prove a new variant of comparison principle for logarithmic $L_2$-small ball probabilities of Gaussian processes. As an application, we obtain logarithmic small ball asymptotics for some well-known processes with smooth covariances.
arxiv
On a set of transformations of Gaussian random functions [PDF]
arXiv, 2008 We consider a set of one-dimensional transformations of Gaussian random functions. Under natural assumptions we obtain a connection between $L_2$-small ball asymptotics of the transformed function and of the original one. Also the explicit Karhunen -- Lo\'eve expansion is obtained for a proper class of Gaussian processes.
arxiv
Discrimination between Gaussian process models: active learning and static constructions. [PDF]
Stat Pap (Berl), 2023 Yousefi E +4 more
europepmc +1 more source
Sharp large deviations for the fractional Ornstein-Uhlenbeck process [PDF]
arXiv, 2008 We investigate the sharp large deviation properties of the energy and the maximum likelihood estimator for the Ornstein-Uhlenbeck process driven by a fractional Brownian motion with Hurst index greater than one half.
arxiv
Pandemic-type failures in multivariate Brownian risk models. [PDF]
Extremes (Boston), 2022 Dȩbicki K, Hashorva E, Kriukov N.
europepmc +1 more source
About Gaussian filtering problems with general exponential quadratic criteria [PDF]
arXiv, 2009 Filtering problems with general exponential quadratic criteria are investigated for Gauss-Markov processes. In this setting, the Linear Exponential Gaussian and Risk-Sensitive filtering problems are solved and it is shown that they may have different solutions.
arxiv
Kaniadakis Functions beyond Statistical Mechanics: Weakest-Link Scaling, Power-Law Tails, and Modified Lognormal Distribution. [PDF]
Entropy (Basel), 2022 Hristopulos DT, Baxevani A.
europepmc +1 more source