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A stochastic “Fubini” lemma and an approximation theorem for
integrals on the plane are used to produce a simulation algorithm
for an anisotropic fractional Brownian sheet. The convergence rate
is given. These results are valuable for any value of the Hurst
parameters Finally, the
approximation process
is iterative on the quarter plane
A sample of such simulations can be used to test estimators
of the parameters αi,i = 1,2.
Coutin, Laure, and Pontier, Monique. "Approximation of the fractional Brownian sheet VIA Ornstein-Uhlenbeck sheet." ESAIM: Probability and Statistics 11 (2007): 115-146. <http://eudml.org/doc/250120>.
@article{Coutin2007, abstract = {
A stochastic “Fubini” lemma and an approximation theorem for
integrals on the plane are used to produce a simulation algorithm
for an anisotropic fractional Brownian sheet. The convergence rate
is given. These results are valuable for any value of the Hurst
parameters $(\alpha_1,\alpha_2)\in ]0,1[^2,\alpha_i\neq\frac\{1\}\{2\}.$ Finally, the
approximation process
is iterative on the quarter plane $\mathbb \{R\}_+^2.$
A sample of such simulations can be used to test estimators
of the parameters αi,i = 1,2.
}, author = {Coutin, Laure, Pontier, Monique}, journal = {ESAIM: Probability and Statistics}, keywords = {random field simulation and approximation; anisotropic
fractional Brownian sheet.; anisotropic fractional Brownian sheet}, language = {eng}, month = {3}, pages = {115-146}, publisher = {EDP Sciences}, title = {Approximation of the fractional Brownian sheet VIA Ornstein-Uhlenbeck sheet}, url = {http://eudml.org/doc/250120}, volume = {11}, year = {2007}, }
TY - JOUR AU - Coutin, Laure AU - Pontier, Monique TI - Approximation of the fractional Brownian sheet VIA Ornstein-Uhlenbeck sheet JO - ESAIM: Probability and Statistics DA - 2007/3// PB - EDP Sciences VL - 11 SP - 115 EP - 146 AB -
A stochastic “Fubini” lemma and an approximation theorem for
integrals on the plane are used to produce a simulation algorithm
for an anisotropic fractional Brownian sheet. The convergence rate
is given. These results are valuable for any value of the Hurst
parameters $(\alpha_1,\alpha_2)\in ]0,1[^2,\alpha_i\neq\frac{1}{2}.$ Finally, the
approximation process
is iterative on the quarter plane $\mathbb {R}_+^2.$
A sample of such simulations can be used to test estimators
of the parameters αi,i = 1,2.
LA - eng KW - random field simulation and approximation; anisotropic
fractional Brownian sheet.; anisotropic fractional Brownian sheet UR - http://eudml.org/doc/250120 ER -
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