# Elliptic self-similar stochastic processes.

Revista Matemática Iberoamericana (2003)

- Volume: 19, Issue: 3, page 767-796
- ISSN: 0213-2230

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topBenassi, 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 -

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