Asymptotic properties and Hausdorff dimensions of fractional Brownian sheets. Zbl 1088.60033
Ayache, Antoine; Xiao, Yimin |
|
2005
|
Fractional Brownian sheet.
(Drap brownien fractionnaire.) Zbl 1006.60029
Ayache, Antoine; Leger, Stéphanie; Pontier, Monique |
|
2002
|
The generalized multifractional Brownian motion. Zbl 0979.60023
Ayache, Antoine; Lévy-Véhel, Jacques |
|
2000
|
Multifractional processes with random exponent. Zbl 1082.60032
Ayache, Antoine; Taqqu, Murad S. |
|
2005
|
Joint continuity of the local times of fractional Brownian sheets. Zbl 1180.60032
Ayache, Antoine; Wu, Dongsheng; Xiao, Yimin |
|
2008
|
Rate optimality of wavelet series approximations of fractional Brownian motion. Zbl 1050.60043
Ayache, Antoine; Taqqu, Murad S. |
|
2003
|
\(L^p\) properties for Gaussian random series. Zbl 1145.60019
Ayache, Antoine; Tzvetkov, Nikolay |
|
2008
|
On the identification of the pointwise Hölder exponent of the generalized multifractional Brownian motion. Zbl 1079.60029
Ayache, Antoine; Lévy Véhel, Jacques |
|
2004
|
Wavelet construction of generalized multifractional processes. Zbl 1123.60022
Ayache, Antoine; Jaffard, Stéphane; Taqqu, Murad S. |
|
2007
|
Linear fractional stable sheets: Wavelet expansion and sample path properties. Zbl 1162.60324
Ayache, Antoine; Roueff, François; Xiao, Yimin |
|
2009
|
Some methods for constructing nonseparable, orthonormal, compactly supported wavelet bases. Zbl 0977.42017
Ayache, Antoine |
|
2001
|
Generalized multifractional Brownian motion: Definition and preliminary results. Zbl 0964.60046
Ayache, Antoine; Lévy Véhel, Jacques |
|
1999
|
Construction of non separable dyadic compactly supported orthonormal wavelet bases for \(L^2(\mathbb{R}^2)\) of arbitrarily high regularity. Zbl 0923.42021
Ayache, Antoine |
|
1999
|
Multiparameter multifractional Brownian motion: local nondeterminism and joint continuity of the local times. Zbl 1268.60048
Ayache, Antoine; Shieh, Narn-Rueih; Xiao, Yimin |
|
2011
|
The generalized multifractional field: A nice tool for the study of the generalized multifractional Brownian motion. Zbl 1031.60026
Ayache, Antoine |
|
2002
|
Hausdorff dimension of the graph of the fractional Brownian sheet. Zbl 1057.60033
Ayache, Antoine |
|
2004
|
Multifractional stochastic fields. Wavelet strategies in multifractional frameworks. Zbl 1429.60001
Ayache, Antoine |
|
2019
|
Linear fractional stable motion: A wavelet estimator of the \(\alpha\) parameter. Zbl 1456.62177
Ayache, Antoine; Hamonier, Julien |
|
2012
|
Local and asymptotic properties of linear fractional stable sheets. Zbl 1112.60038
Ayache, Antoine; Roueff, François; Xiao, Yimin |
|
2007
|
A central limit theorem for the generalized quadratic variation of the step fractional Brownian motion. Zbl 1115.60024
Ayache, Antoine; Bertrand, Pierre; Lévy-Véhel, Jacques |
|
2007
|
Continuous Gaussian multifractional processes with random pointwise Hölder regularity. Zbl 1296.60091
Ayache, Antoine |
|
2013
|
Estimation of cyclic long-memory parameters. Zbl 1444.62097
Alomari, Huda Mohammed; Ayache, Antoine; Fradon, Myriam; Olenko, Andriy |
|
2020
|
Linear multifractional stable motion: fine path properties. Zbl 1312.60041
Ayache, Antoine; Hamonier, Julien |
|
2014
|
Lower bound for local oscillations of Hermite processes. Zbl 1444.60028
Ayache, Antoine |
|
2020
|
Les ondelettes à la conquête du drap brownien fractionnaire. (Wavelets conquering the fractional Brownian field). Zbl 1014.60057
Ayache, Antoine; Leger, Stéphanie; Pontier, Monique |
|
2002
|
Sharp estimates on the tail behavior of a multistable distribution. Zbl 1269.60017
Ayache, Antoine |
|
2013
|
A process very similar to multifractional Brownian motion. Zbl 1215.60029
Ayache, Antoine; Bertrand, Pierre R. |
|
2010
|
Asymptotic normality of simultaneous estimators of cyclic long-memory processes. Zbl 1498.62175
Ayache, Antoine; Fradon, Myriam; Nanayakkara, Ravindi; Olenko, Andriy |
|
2022
|
Joint continuity of the local times of linear fractional stable sheets. Zbl 1117.60042
Ayache, Antoine; Roueff, François; Xiao, Yimin |
|
2007
|
Approximation of Gaussian random fields: General results and optimal wavelet representation of the Lévy fractional motion. Zbl 1140.60028
Ayache, Antoine; Linde, Werner |
|
2008
|
Wavelet-type expansion of the generalized Rosenblatt process and its rate of convergence. Zbl 1457.60055
Ayache, Antoine; Esmili, Yassine |
|
2020
|
Different possible behaviors of wavelet leaders of the Brownian motion. Zbl 1459.60167
Ayache, Antoine; Esser, Céline; Kleyntssens, Thomas |
|
2019
|
Construction of non-separable compactly supported orthonormal wavelet bases for \(L^2(\mathbb{R}^2)\) with arbitrarily high regularity.
(Construction de bases orthonormées d’ondelettes de \(L^2(\mathbb{R}^2)\) non séparables, à support compact et de régularité arbitrairement grande.) Zbl 0896.46005
Ayache, Antoine |
|
1997
|
Uniformly and strongly consistent estimation for the Hurst function of a linear multifractional stable motion. Zbl 1378.62052
Ayache, Antoine; Hamonier, Julien |
|
2017
|
Harmonizable fractional stable fields: local nondeterminism and joint continuity of the local times. Zbl 1329.60133
Ayache, Antoine; Xiao, Yimin |
|
2016
|
Linear multifractional stable motion: wavelet estimation of \(H(\cdot)\) and \(\alpha\) parameters. Zbl 1321.60076
Ayache, Antoine; Hamonier, Julien |
|
2015
|
A new multifractional process with random exponent. Zbl 1409.60059
Ayache, Antoine; Esser, Céline; Hamonier, Julien |
|
2018
|
Discretization error of wavelet coefficient for fractal like processes. Zbl 1216.62146
Ayache, Antoine; Bertrand, Pierre Raphael |
|
2011
|
A Fourier formulation of the Frostman criterion for random graphs and its applications to wavelet series. Zbl 1039.42029
Ayache, Antoine; Roueff, François |
|
2003
|
Regularity and identifications of generalized multifractional Gaussian processes. Zbl 1076.60026
Ayache, Antoine; Benassi, Albert; Cohen, Serge; Lévy-Véhel, Jacques |
|
2005
|
Series representations of fractional Gaussian processes by trigonometric and Haar systems. Zbl 1193.60051
Linde, Werner; Ayache, Antoine |
|
2009
|
Moving average multifractional processes with random exponent: lower bounds for local oscillations. Zbl 1492.60095
Ayache, Antoine; Bouly, Florent |
|
2022
|
Hölder exponents of arbitrary functions. Zbl 1203.26021
Ayache, Antoine; Jaffard, Stéphane |
|
2010
|
Identification and series decomposition of anisotropic Gaussian fields. Zbl 1181.60056
Ayache, A.; Bonami, A.; Estrade, A. |
|
2009
|
Stochastic volatility and multifractional Brownian motion. Zbl 1247.91205
Ayache, Antoine; Peng, Qidi |
|
2012
|
Stationary increments harmonizable stable fields: upper estimates on path behaviour. Zbl 1409.60077
Ayache, Antoine; Boutard, Geoffrey |
|
2017
|
On the monofractality of many stationary continuous Gaussian fields. Zbl 1480.60099
Ayache, Antoine |
|
2021
|
On local path behavior of surgailis multifractional processes. Zbl 1495.60021
Ayache, A.; Bouly, F. |
|
2022
|
Wavelet series representation and geometric properties of harmonizable fractional stable sheets. Zbl 1490.60126
Ayache, Antoine; Shieh, Narn-Rueih; Xiao, Yimin |
|
2020
|
Behaviour of linear multifractional stable motion: membership of a critical Hölder space. Zbl 1394.60031
Ayache, Antoine; Hamonier, Julien |
|
2017
|
Wavelet analysis of a multifractional process in an arbitrary Wiener chaos. Zbl 1488.60091
Ayache, A.; Esmili, Y. |
|
2019
|
Processes with prescribed local regularity.
(Processus à régularité locale prescrite.) Zbl 0988.60028
Ayache, Antoine; Lévy Véhel, Jacques |
|
2001
|
A geometrical solution of a problem on wavelets. Zbl 0964.42010
Ayache, Antoine |
|
2000
|
A useful result related with zeros of continuous compactly supported mother wavelets. Zbl 1373.42042
Ayache, Antoine; Esser, Céline |
|
2017
|
Asymptotic normality of simultaneous estimators of cyclic long-memory processes. Zbl 1498.62175
Ayache, Antoine; Fradon, Myriam; Nanayakkara, Ravindi; Olenko, Andriy |
|
2022
|
Moving average multifractional processes with random exponent: lower bounds for local oscillations. Zbl 1492.60095
Ayache, Antoine; Bouly, Florent |
|
2022
|
On local path behavior of surgailis multifractional processes. Zbl 1495.60021
Ayache, A.; Bouly, F. |
|
2022
|
On the monofractality of many stationary continuous Gaussian fields. Zbl 1480.60099
Ayache, Antoine |
|
2021
|
Estimation of cyclic long-memory parameters. Zbl 1444.62097
Alomari, Huda Mohammed; Ayache, Antoine; Fradon, Myriam; Olenko, Andriy |
|
2020
|
Lower bound for local oscillations of Hermite processes. Zbl 1444.60028
Ayache, Antoine |
|
2020
|
Wavelet-type expansion of the generalized Rosenblatt process and its rate of convergence. Zbl 1457.60055
Ayache, Antoine; Esmili, Yassine |
|
2020
|
Wavelet series representation and geometric properties of harmonizable fractional stable sheets. Zbl 1490.60126
Ayache, Antoine; Shieh, Narn-Rueih; Xiao, Yimin |
|
2020
|
Multifractional stochastic fields. Wavelet strategies in multifractional frameworks. Zbl 1429.60001
Ayache, Antoine |
|
2019
|
Different possible behaviors of wavelet leaders of the Brownian motion. Zbl 1459.60167
Ayache, Antoine; Esser, Céline; Kleyntssens, Thomas |
|
2019
|
Wavelet analysis of a multifractional process in an arbitrary Wiener chaos. Zbl 1488.60091
Ayache, A.; Esmili, Y. |
|
2019
|
A new multifractional process with random exponent. Zbl 1409.60059
Ayache, Antoine; Esser, Céline; Hamonier, Julien |
|
2018
|
Uniformly and strongly consistent estimation for the Hurst function of a linear multifractional stable motion. Zbl 1378.62052
Ayache, Antoine; Hamonier, Julien |
|
2017
|
Stationary increments harmonizable stable fields: upper estimates on path behaviour. Zbl 1409.60077
Ayache, Antoine; Boutard, Geoffrey |
|
2017
|
Behaviour of linear multifractional stable motion: membership of a critical Hölder space. Zbl 1394.60031
Ayache, Antoine; Hamonier, Julien |
|
2017
|
A useful result related with zeros of continuous compactly supported mother wavelets. Zbl 1373.42042
Ayache, Antoine; Esser, Céline |
|
2017
|
Harmonizable fractional stable fields: local nondeterminism and joint continuity of the local times. Zbl 1329.60133
Ayache, Antoine; Xiao, Yimin |
|
2016
|
Linear multifractional stable motion: wavelet estimation of \(H(\cdot)\) and \(\alpha\) parameters. Zbl 1321.60076
Ayache, Antoine; Hamonier, Julien |
|
2015
|
Linear multifractional stable motion: fine path properties. Zbl 1312.60041
Ayache, Antoine; Hamonier, Julien |
|
2014
|
Continuous Gaussian multifractional processes with random pointwise Hölder regularity. Zbl 1296.60091
Ayache, Antoine |
|
2013
|
Sharp estimates on the tail behavior of a multistable distribution. Zbl 1269.60017
Ayache, Antoine |
|
2013
|
Linear fractional stable motion: A wavelet estimator of the \(\alpha\) parameter. Zbl 1456.62177
Ayache, Antoine; Hamonier, Julien |
|
2012
|
Stochastic volatility and multifractional Brownian motion. Zbl 1247.91205
Ayache, Antoine; Peng, Qidi |
|
2012
|
Multiparameter multifractional Brownian motion: local nondeterminism and joint continuity of the local times. Zbl 1268.60048
Ayache, Antoine; Shieh, Narn-Rueih; Xiao, Yimin |
|
2011
|
Discretization error of wavelet coefficient for fractal like processes. Zbl 1216.62146
Ayache, Antoine; Bertrand, Pierre Raphael |
|
2011
|
A process very similar to multifractional Brownian motion. Zbl 1215.60029
Ayache, Antoine; Bertrand, Pierre R. |
|
2010
|
Hölder exponents of arbitrary functions. Zbl 1203.26021
Ayache, Antoine; Jaffard, Stéphane |
|
2010
|
Linear fractional stable sheets: Wavelet expansion and sample path properties. Zbl 1162.60324
Ayache, Antoine; Roueff, François; Xiao, Yimin |
|
2009
|
Series representations of fractional Gaussian processes by trigonometric and Haar systems. Zbl 1193.60051
Linde, Werner; Ayache, Antoine |
|
2009
|
Identification and series decomposition of anisotropic Gaussian fields. Zbl 1181.60056
Ayache, A.; Bonami, A.; Estrade, A. |
|
2009
|
Joint continuity of the local times of fractional Brownian sheets. Zbl 1180.60032
Ayache, Antoine; Wu, Dongsheng; Xiao, Yimin |
|
2008
|
\(L^p\) properties for Gaussian random series. Zbl 1145.60019
Ayache, Antoine; Tzvetkov, Nikolay |
|
2008
|
Approximation of Gaussian random fields: General results and optimal wavelet representation of the Lévy fractional motion. Zbl 1140.60028
Ayache, Antoine; Linde, Werner |
|
2008
|
Wavelet construction of generalized multifractional processes. Zbl 1123.60022
Ayache, Antoine; Jaffard, Stéphane; Taqqu, Murad S. |
|
2007
|
Local and asymptotic properties of linear fractional stable sheets. Zbl 1112.60038
Ayache, Antoine; Roueff, François; Xiao, Yimin |
|
2007
|
A central limit theorem for the generalized quadratic variation of the step fractional Brownian motion. Zbl 1115.60024
Ayache, Antoine; Bertrand, Pierre; Lévy-Véhel, Jacques |
|
2007
|
Joint continuity of the local times of linear fractional stable sheets. Zbl 1117.60042
Ayache, Antoine; Roueff, François; Xiao, Yimin |
|
2007
|
Asymptotic properties and Hausdorff dimensions of fractional Brownian sheets. Zbl 1088.60033
Ayache, Antoine; Xiao, Yimin |
|
2005
|
Multifractional processes with random exponent. Zbl 1082.60032
Ayache, Antoine; Taqqu, Murad S. |
|
2005
|
Regularity and identifications of generalized multifractional Gaussian processes. Zbl 1076.60026
Ayache, Antoine; Benassi, Albert; Cohen, Serge; Lévy-Véhel, Jacques |
|
2005
|
On the identification of the pointwise Hölder exponent of the generalized multifractional Brownian motion. Zbl 1079.60029
Ayache, Antoine; Lévy Véhel, Jacques |
|
2004
|
Hausdorff dimension of the graph of the fractional Brownian sheet. Zbl 1057.60033
Ayache, Antoine |
|
2004
|
Rate optimality of wavelet series approximations of fractional Brownian motion. Zbl 1050.60043
Ayache, Antoine; Taqqu, Murad S. |
|
2003
|
A Fourier formulation of the Frostman criterion for random graphs and its applications to wavelet series. Zbl 1039.42029
Ayache, Antoine; Roueff, François |
|
2003
|
Fractional Brownian sheet.
(Drap brownien fractionnaire.) Zbl 1006.60029
Ayache, Antoine; Leger, Stéphanie; Pontier, Monique |
|
2002
|
The generalized multifractional field: A nice tool for the study of the generalized multifractional Brownian motion. Zbl 1031.60026
Ayache, Antoine |
|
2002
|
Les ondelettes à la conquête du drap brownien fractionnaire. (Wavelets conquering the fractional Brownian field). Zbl 1014.60057
Ayache, Antoine; Leger, Stéphanie; Pontier, Monique |
|
2002
|
Some methods for constructing nonseparable, orthonormal, compactly supported wavelet bases. Zbl 0977.42017
Ayache, Antoine |
|
2001
|
Processes with prescribed local regularity.
(Processus à régularité locale prescrite.) Zbl 0988.60028
Ayache, Antoine; Lévy Véhel, Jacques |
|
2001
|
The generalized multifractional Brownian motion. Zbl 0979.60023
Ayache, Antoine; Lévy-Véhel, Jacques |
|
2000
|
A geometrical solution of a problem on wavelets. Zbl 0964.42010
Ayache, Antoine |
|
2000
|
Generalized multifractional Brownian motion: Definition and preliminary results. Zbl 0964.60046
Ayache, Antoine; Lévy Véhel, Jacques |
|
1999
|
Construction of non separable dyadic compactly supported orthonormal wavelet bases for \(L^2(\mathbb{R}^2)\) of arbitrarily high regularity. Zbl 0923.42021
Ayache, Antoine |
|
1999
|
Construction of non-separable compactly supported orthonormal wavelet bases for \(L^2(\mathbb{R}^2)\) with arbitrarily high regularity.
(Construction de bases orthonormées d’ondelettes de \(L^2(\mathbb{R}^2)\) non séparables, à support compact et de régularité arbitrairement grande.) Zbl 0896.46005
Ayache, Antoine |
|
1997
|