scholarly journals From infinite urn schemes to decompositions of self-similar Gaussian processes

2016 ◽  
Vol 21 (0) ◽  
Author(s):  
Olivier Durieu ◽  
Yizao Wang
Keyword(s):  
Gaussian Processes ◽  
Self Similar

scholarly journals Symmetric Stochastic Integrals with Respect to a Class of Self-similar Gaussian Processes

2018 ◽  
Vol 32 (3) ◽  
pp. 1105-1144
Author(s):  
Daniel Harnett ◽  
Arturo Jaramillo ◽  
David Nualart
Keyword(s):  
Gaussian Processes ◽  
Stochastic Integrals ◽  
Self Similar

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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