Elliptic self-similar stochastic processes.

Benassi, Albert, and Roux, Daniel. "Elliptic self-similar stochastic processes.." Revista Matemática Iberoamericana 19.3 (2003): 767-796. <http://eudml.org/doc/39674>.

@article{Benassi2003,
abstract = {Let M be a random measure and L be an elliptic pseudo-differential operator on Rd. We study the solution of the stochastic problem LX = M, X(O) = O when some homogeneity and integrability conditions are assumed. If M is a Gaussian measure the process X belongs to the class of Elliptic Gaussian Processes which has already been studied. Here the law of M is not necessarily Gaussian. We characterize the solutions X which are self-similar and with stationary increments in terms of the driving mcasure M. Then we use appropriate wavelet bases to expand these solutions and we give regularity results. In the last section it is shown how a percolation forest can help with constructing a self-similar Elliptic Process with non stable law.},
author = {Benassi, Albert, Roux, Daniel},
journal = {Revista Matemática Iberoamericana},
keywords = {Procesos estocásticos; Operadores pseudodiferenciales; Operadores elípticos; Ondículas; elliptic processes; self-similar processes with stationary increments; elliptic pseudo-differential operator; wavelet basis; regularity of sample paths; percolation tree; intermittency},
language = {eng},
number = {3},
pages = {767-796},
title = {Elliptic self-similar stochastic processes.},
url = {http://eudml.org/doc/39674},
volume = {19},
year = {2003},
}

TY - JOUR
AU - Benassi, Albert
AU - Roux, Daniel
TI - Elliptic self-similar stochastic processes.
JO - Revista Matemática Iberoamericana
PY - 2003
VL - 19
IS - 3
SP - 767
EP - 796
AB - Let M be a random measure and L be an elliptic pseudo-differential operator on Rd. We study the solution of the stochastic problem LX = M, X(O) = O when some homogeneity and integrability conditions are assumed. If M is a Gaussian measure the process X belongs to the class of Elliptic Gaussian Processes which has already been studied. Here the law of M is not necessarily Gaussian. We characterize the solutions X which are self-similar and with stationary increments in terms of the driving mcasure M. Then we use appropriate wavelet bases to expand these solutions and we give regularity results. In the last section it is shown how a percolation forest can help with constructing a self-similar Elliptic Process with non stable law.
LA - eng
KW - Procesos estocásticos; Operadores pseudodiferenciales; Operadores elípticos; Ondículas; elliptic processes; self-similar processes with stationary increments; elliptic pseudo-differential operator; wavelet basis; regularity of sample paths; percolation tree; intermittency
UR - http://eudml.org/doc/39674
ER -