scholarly journals Nonstationary self‐similar Gaussian processes as scaling limits of power‐law shot noise processes and generalizations of fractional Brownian motion

2019 ◽  
Vol 2 (2) ◽  
pp. 95-112 ◽  
Author(s):  
Guodong Pang ◽  
Murad S. Taqqu
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Power Law ◽  
Shot Noise ◽  
Gaussian Processes ◽  
Scaling Limits ◽  
Self Similar

scholarly journals Survival Exponents for Some Gaussian Processes

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
G. Molchan
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Power Law ◽  
Gaussian Processes ◽  
Similar Process ◽  
Fixed Level ◽  
Long Time ◽  
Self Similar

The problem is a power-law asymptotics of the probability that a self-similar process does not exceed a fixed level during long time. The exponent in such asymptotics is estimated for some Gaussian processes, including the fractional Brownian motion (FBM) in , and the integrated FBM in , .

scholarly journals On Scaling Limits of Power Law Shot-Noise Fields

2015 ◽  
Vol 31 (2) ◽  
pp. 187-207 ◽  
Author(s):  
François Baccelli ◽  
Anup Biswas
Keyword(s):  
Power Law ◽  
Shot Noise ◽  
Scaling Limits

scholarly journals A DYNAMICAL APPROACH TO FRACTIONAL BROWNIAN MOTION

Fractals ◽  
1994 ◽  
Vol 02 (01) ◽  
pp. 81-94 ◽  
Author(s):  
RICCARDO MANNELLA ◽  
PAOLO GRIGOLINI ◽  
BRUCE J. WEST
Keyword(s):  
Dynamical System ◽  
Asymptotic Behavior ◽  
Brownian Motion ◽  
Correlation Function ◽  
Fractional Brownian Motion ◽  
Gaussian Processes ◽  
The Other ◽  
Hurst Coefficient ◽  
And Diffusion ◽  
Clear Relation

Herein we develop a dynamical foundation for fractional Brownian motion. A clear relation is established between the asymptotic behavior of the correlation function and diffusion in a dynamical system. Then, assuming that scaling is applicable, we establish a connection between diffusion (either standard or anomalous) and the dynamical indicator known as the Hurst coefficient. We argue on the basis of numerical simulations that although we have been able to prove scaling only for "Gaussian" processes, our conclusions may well apply to a wider class of systems. On the other hand, systems exist for which scaling might not hold, so we speculate on the possible consequences of the various relations derived in the paper on such systems.

scholarly journals Some fractional and multifractional Gaussian processes: A brief introduction

2015 ◽  
Vol 36 ◽  
pp. 1560001
Author(s):  
S. C. Lim ◽  
C. H. Eab
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Gaussian Processes ◽  
Natural Phenomena ◽  
Liouville Type ◽  
Multifractional Brownian Motion

This paper gives a brief introduction to some important fractional and multifractional Gaussian processes commonly used in modelling natural phenomena and man-made systems. The processes include fractional Brownian motion (both standard and the Riemann-Liouville type), multifractional Brownian motion, fractional and multifractional Ornstein-Uhlenbeck processes, fractional and mutifractional Reisz-Bessel motion. Possible applications of these processes are briefly mentioned.

On the Lamperti transform of the fractional Brownian sheet

2016 ◽  
Vol 19 (6) ◽  
Author(s):  
Marwa Khalil ◽  
Ciprian Tudor ◽  
Mounir Zili
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Stochastic Differential Equation ◽  
Gaussian Processes ◽  
Stationary Process ◽  
Similar Process ◽  
Brownian Sheet ◽  
Fractional Brownian Sheet ◽  
Self Similar ◽  
Strictly Stationary Process

AbstractIn 1962 Lamperti introduced a transformation that associates to every non-trivial self-similar process a strictly stationary process. This transform has been widely studied for Gaussian processes and in particular for fractional Brownian motion. Our aim is to analyze various properties of the Lamperti transform of the fractional Brownian sheet. We give the stochastic differential equation satisfied by this transform and we represent it as a series of independent Ornstein-Uhlenbeck sheets.

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