scholarly journals Remarks on the Poisson Stochastic Process (II)

1953 ◽  
Vol 13 (1) ◽  
pp. 130-136 ◽  
Author(s):  
E. Marczewski
Keyword(s):  
Stochastic Process ◽  
Poisson Stochastic Process

scholarly journals Remarks on the Poisson Stochastic Process, I

1953 ◽  
Vol 13 (1) ◽  
pp. 122-129 ◽  
Author(s):  
K. Florek ◽  
E. Marczewski ◽  
C. Ryll-Nardzewski
Keyword(s):  
Stochastic Process ◽  
Poisson Stochastic Process

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.

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