A Uniform Functional Law of the Logarithm for a Local Gaussian Process

2003 ◽  
pp. 135-151
Author(s):  
David M. Mason
Keyword(s):  
Gaussian Process ◽  
Law Of The Logarithm

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

A Stochastic Model for the Inheritance of the Cancer Proneness Phenotype

1987 ◽  
Vol 26 (03) ◽  
pp. 117-123
Author(s):  
P. Tautu ◽  
G. Wagner
Keyword(s):  
Stochastic Model ◽  
Gaussian Process ◽  
Covariance Function ◽  
Neoplastic Disease ◽  
Disease Phenotype ◽  
Probabilistic Representation ◽  
Temporal Behaviour ◽  
Continuous Trait ◽  
Continuous Parameter ◽  
Level Zero

SummaryA continuous parameter, stationary Gaussian process is introduced as a first approach to the probabilistic representation of the phenotype inheritance process. With some specific assumptions about the components of the covariance function, it may describe the temporal behaviour of the “cancer-proneness phenotype” (CPF) as a quantitative continuous trait. Upcrossing a fixed level (“threshold”) u and reaching level zero are the extremes of the Gaussian process considered; it is assumed that they might be interpreted as the transformation of CPF into a “neoplastic disease phenotype” or as the non-proneness to cancer, respectively.

Identification of Continuous-time Nonlinear Systems via Local Gaussian Process Models

2014 ◽  
Vol 134 (11) ◽  
pp. 1708-1715
Author(s):  
Tomohiro Hachino ◽  
Kazuhiro Matsushita ◽  
Hitoshi Takata ◽  
Seiji Fukushima ◽  
Yasutaka Igarashi
Keyword(s):  
Nonlinear Systems ◽  
Gaussian Process ◽  
Continuous Time ◽  
Process Models ◽  
Gaussian Process Models

INVERSE UNCERTAINTY QUANTIFICATION OF A CELL MODEL USING A GAUSSIAN PROCESS METAMODEL

2020 ◽  
Vol 10 (4) ◽  
pp. 333-349
Author(s):  
Kevin de Vries ◽  
Anna Nikishova ◽  
Benjamin Czaja ◽  
Gábor Závodszky ◽  
Alfons G. Hoekstra
Keyword(s):  
Gaussian Process ◽  
Uncertainty Quantification ◽  
Cell Model ◽  
A Cell
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