-
1
-
-
0002430828
-
Wavelets, spectrum analysis and 1/f processes
-
P. Abry, P. Gonçalvès and P. Flandrin, Wavelets, spectrum analysis and 1/f processes. Lect. Note Stat. 103 (1995) 15-29.
-
(1995)
Lect. Note Stat.
, vol.103
, pp. 15-29
-
-
Abry, P.1
Gonçalvès, P.2
Flandrin, P.3
-
3
-
-
1642419174
-
On the identification of the pointwise Holder exponent of the generalized multifractional Brownian motion
-
A. Ayache and J. Levy-Vehel, On the identification of the pointwise Holder exponent of the generalized multifractional Brownian motion. Stoc. Proc. Appl. 111 (2004) 119-156.
-
(2004)
Stoc. Proc. Appl.
, vol.111
, pp. 119-156
-
-
Ayache, A.1
Levy-Vehel, J.2
-
4
-
-
33749515596
-
A central limit theorem for the generalized quadratic variation of the step fractional Brownian
-
A. Ayache, P. Bertrand and J. Levy-Vehel, A central limit theorem for the generalized quadratic variation of the step fractional Brownian. Stat. Inference Stoch. Process. 10 (2007) 1-27.
-
(2007)
Stat. Inference Stoch. Process.
, vol.10
, pp. 1-27
-
-
Ayache, A.1
Bertrand, P.2
Levy-Vehel, J.3
-
5
-
-
0000625581
-
Testing for the presence of self-similarity of Gaussian time series having stationary increments
-
J.-M. Bardet, Testing for the presence of self-similarity of Gaussian time series having stationary increments. J. Time Ser. Anal. 25 (2000) 497-515.
-
(2000)
J. Time Ser. Anal.
, vol.25
, pp. 497-515
-
-
Bardet, J.-M.1
-
6
-
-
33845704773
-
Identification of the multiscale fractional Brownian motion with biomechanical applications
-
J.-M. Bardet and P. Bertrand, Identification of the multiscale fractional Brownian motion with biomechanical applications. J. Time Ser. Anal. 28 (2007) 1-52.
-
(2007)
J. Time Ser. Anal.
, vol.28
, pp. 1-52
-
-
Bardet, J.-M.1
Bertrand, P.2
-
8
-
-
0031496443
-
Gaussian processes and Pseudodifferential Elliptic operators
-
A. Benassi, S. Jaffard and D. Roux, Gaussian processes and Pseudodifferential Elliptic operators. Revista Mathematica Iberoam. 13 (1997) 19-90.
-
(1997)
Revista Mathematica Iberoam.
, vol.13
, pp. 19-90
-
-
Benassi, A.1
Jaffard, S.2
Roux, D.3
-
9
-
-
0032555366
-
Identifying the multifractional function of a Gaussian process
-
A. Benassi, S. Cohen and J. Istas, Identifying the multifractional function of a Gaussian process. Stat. Probab. Lett. 39 (1998) 337-345.
-
(1998)
Stat. Probab. Lett.
, vol.39
, pp. 337-345
-
-
Benassi, A.1
Cohen, S.2
Istas, J.3
-
12
-
-
0037874979
-
Identification and properties of real harmonizable fractional Levy motions
-
A. Benassi, S. Cohen and J. Istas, Identification and properties of real harmonizable fractional Levy motions. Bernoulli 8 (2002) 97-115.
-
(2002)
Bernoulli
, vol.8
, pp. 97-115
-
-
Benassi, A.1
Cohen, S.2
Istas, J.3
-
13
-
-
13344278798
-
On roughness indices for fractional fields
-
A. Benassi, S. Cohen and J. Istas, On roughness indices for fractional fields. Bernoulli 10 (2004) 357-373.
-
(2004)
Bernoulli
, vol.10
, pp. 357-373
-
-
Benassi, A.1
Cohen, S.2
Istas, J.3
-
14
-
-
23244442846
-
Quadratic variations along irregular subdivisions for Gaussian processes
-
A. Begyn, Quadratic variations along irregular subdivisions for Gaussian processes. Electron. J. Probab. 10 (2005) 691-717.
-
(2005)
Electron. J. Probab.
, vol.10
, pp. 691-717
-
-
Begyn, A.1
-
15
-
-
47249150060
-
Asymptotic expansion and central limit theorem for quadratic variations of Gaussian processes
-
A. Begyn, Asymptotic expansion and central limit theorem for quadratic variations of Gaussian processes. Bernoulli 13 (2007) 712-753.
-
(2007)
Bernoulli
, vol.13
, pp. 712-753
-
-
Begyn, A.1
-
16
-
-
35348961996
-
Functional limit theorems for generalized quadratic variations of Gaussian processes
-
A. Begyn, Functional limit theorems for generalized quadratic variations of Gaussian processes. Stoc. Proc. Appl. 117 (2007) 1848-1869.
-
(2007)
Stoc. Proc. Appl.
, vol.117
, pp. 1848-1869
-
-
Begyn, A.1
-
18
-
-
0041350470
-
Anisotropic analysis of Gaussian models
-
A. Bonami and A. Estrade, Anisotropic analysis of Gaussian models. J. Fourier Anal. Appl. 9 (2004) 215-236.
-
(2004)
J. Fourier Anal. Appl.
, vol.9
, pp. 215-236
-
-
Bonami, A.1
Estrade, A.2
-
19
-
-
0041859748
-
On the angular defect of triangulations and the pointwise approximation of curvatures, curves and surfaces’02
-
V. Borrelli, F. Cazals and J.-M. Morvan, On the angular defect of triangulations and the pointwise approximation of curvatures, curves and surfaces’02. Comput. Aid. Geom. Des. 20 319-341.
-
Comput. Aid. Geom. Des.
, vol.20
, pp. 319-341
-
-
Borrelli, V.1
Cazals, F.2
Morvan, J.-M.3
-
22
-
-
77958128357
-
On simulation of fractional Brownian motion indexed by a manifold
-
A. Brouste, J. Istas and S. Lambert-Lacroix, On simulation of fractional Brownian motion indexed by a manifold. J. Stat. Soft. 36 (2010).
-
(2010)
J. Stat. Soft.
, pp. 36
-
-
Brouste, A.1
Istas, J.2
Lambert-Lacroix, S.3
-
23
-
-
0040785045
-
Levy’s Brownian motion of several parameters and generalized white noise
-
N. Chentsov, Levy’s Brownian motion of several parameters and generalized white noise. Theory Probab. Appl. 2 (1957) 265-266.
-
(1957)
Theory Probab. Appl.
, vol.2
, pp. 265-266
-
-
Chentsov, N.1
-
24
-
-
0012307377
-
Simulation and identification of the fractional Brownian motion: A bibliographical and comparative study
-
J.-F. Coeurjolly, Simulation and identification of the fractional Brownian motion: A bibliographical and comparative study. J. Stat. Software 5 (2000) 1-53.
-
(2000)
J. Stat. Software
, vol.5
, pp. 1-53
-
-
Coeurjolly, J.-F.1
-
25
-
-
14844364925
-
Estimating the parameters of a fractional Brownian Motion by discrete variations of its sample paths
-
J.-F. Coeurjolly, Estimating the parameters of a fractional Brownian Motion by discrete variations of its sample paths. Stat. Inference Stoch. Process. 4 (2001) 199-227.
-
(2001)
Stat. Inference Stoch. Process.
, vol.4
, pp. 199-227
-
-
Coeurjolly, J.-F.1
-
26
-
-
33947392024
-
Identification of multifractional Brownian motion
-
J.-F. Coeurjolly, Identification of multifractional Brownian motion. Bernoulli 11 (2005) 987-1008.
-
(2005)
Bernoulli
, vol.11
, pp. 987-1008
-
-
Coeurjolly, J.-F.1
-
27
-
-
51049085803
-
Hurst exponent estimation of locally self-similar Gaussian processes using sample quantiles
-
J.-F. Coeurjolly, Hurst exponent estimation of locally self-similar Gaussian processes using sample quantiles. Ann. Statist. 36 (2008) 1404-1434.
-
(2008)
Ann. Statist.
, vol.36
, pp. 1404-1434
-
-
Coeurjolly, J.-F.1
-
28
-
-
0035402790
-
Cramer-Rao bounds for fractional Brownian motions
-
J.-F. Coeurjolly and J. Istas, Cramer-Rao bounds for fractional Brownian motions. Stat. Probab. Lett. 53 (2001) 435-447.
-
(2001)
Stat. Probab. Lett.
, vol.53
, pp. 435-447
-
-
Coeurjolly, J.-F.1
Istas, J.2
-
33
-
-
31444434274
-
Singularity functions for fractional processes: Application to the fractional brownian sheet
-
S. Cohen, X. Guyon, O. Perrin and M. Pontier, Singularity functions for fractional processes: Application to the fractional brownian sheet. Ann. Inst. Henri Poincarée 42 (2006) 187-205.
-
(2006)
Ann. Inst. Henri Poincarée
, vol.42
, pp. 187-205
-
-
Cohen, S.1
Guyon, X.2
Perrin, O.3
Pontier, M.4
-
35
-
-
0001318609
-
Efficient parameter estimation for self-similar processes
-
R. Dalhaus, Efficient parameter estimation for self-similar processes. Ann. Statist. 17 (1989) 1749-1766.
-
(1989)
Ann. Statist.
, vol.17
, pp. 1749-1766
-
-
Dalhaus, R.1
-
36
-
-
84990575058
-
Orthonormal bases of compactly supported wavelets
-
I. Daubechies, Orthonormal bases of compactly supported wavelets. Commun. Pure Appl. Math. 41 (1988) 909-996.
-
(1988)
Commun. Pure Appl. Math.
, vol.41
, pp. 909-996
-
-
Daubechies, I.1
-
37
-
-
0142105892
-
Partial autocorrelation function of a nonstationary time series
-
S. Degerine and S. Lambert-Lacroix, Partial autocorrelation function of a nonstationary time series. J. Multiv. Anal. (2003) 46-59.
-
(2003)
J. Multiv. Anal
, pp. 46-59
-
-
Degerine, S.1
Lambert-Lacroix, S.2
-
38
-
-
0002566869
-
Automodel generalized random fields and their renorm group
-
edited by R.L. Dobrushin and Ya. G. Sinai. Dekker, New York
-
R.L. Dobrushin, Automodel generalized random fields and their renorm group, in Multicomponent Random Systems, edited by R.L. Dobrushin and Ya. G. Sinai. Dekker, New York (1980) 153-198.
-
(1980)
Multicomponent Random Systems
, pp. 153-198
-
-
Dobrushin, R.L.1
-
41
-
-
0038623727
-
Tangent fields and the local structure of random fields
-
K. Falconer, Tangent fields and the local structure of random fields. J. Theor. Probab. 15 (2002) 731-750.
-
(2002)
J. Theor. Probab.
, vol.15
, pp. 731-750
-
-
Falconer, K.1
-
42
-
-
0037900816
-
The local structure of random processes
-
K. Falconer, The local structure of random processes. J. Lond. Math. Soc. 67 (2003) 657-672.
-
(2003)
J. Lond. Math. Soc.
, vol.67
, pp. 657-672
-
-
Falconer, K.1
-
43
-
-
29244454714
-
Fonction brownienne sur une variete riemannienne
-
J. Faraut, Fonction brownienne sur une variete riemannienne. Séminaire de probabilités de Strasbourg 7 (1973) 61-76.
-
(1973)
Séminaire De probabilités De Strasbourg
, vol.7
, pp. 61-76
-
-
Faraut, J.1
-
44
-
-
0001213621
-
Distances hilbertiennes invariantes sur un espace homogene
-
J. Faraut and H. Harzallah, Distances hilbertiennes invariantes sur un espace homogene. Ann. Inst. Fourier 24 (1974) 171-217.
-
(1974)
Ann. Inst. Fourier
, vol.24
, pp. 171-217
-
-
Faraut, J.1
Harzallah, H.2
-
46
-
-
0013112619
-
Positive definite kernels on homogeneous spaces and certain stochastic processes related to Levy’s Brownian motion of several parameters
-
R. Gangolli, Positive definite kernels on homogeneous spaces and certain stochastic processes related to Levy’s Brownian motion of several parameters. Ann. Inst. Henri Poincare 3 (1967) 121-226.
-
(1967)
Ann. Inst. Henri Poincare
, vol.3
, pp. 121-226
-
-
Gangolli, R.1
-
47
-
-
0000138698
-
Convergence en loi des H-variations d’un processus gaussien stationnaire
-
X. Guyon and J. Leon, Convergence en loi des H-variations d’un processus gaussien stationnaire. Ann. Inst. Henri Poincare 25 (1989) 265-282.
-
(1989)
Ann. Inst. Henri Poincare
, vol.25
, pp. 265-282
-
-
Guyon, X.1
Leon, J.2
-
49
-
-
33845645826
-
A set-indexed fractional Brownian motion
-
E. Herbin and E. Merzbach, A set-indexed fractional Brownian motion. J. Theor. Probab. 19 (2006) 337-364.
-
(2006)
J. Theor. Probab.
, vol.19
, pp. 337-364
-
-
Herbin, E.1
Merzbach, E.2
-
50
-
-
70350719885
-
Stationarity and self-similarity characterization of the set-indexed fractional Brownian motion
-
E. Herbin and E. Merzbach, Stationarity and self-similarity characterization of the set-indexed fractional Brownian motion. J. Theor. Probab. 22 (2009) 1010-1029.
-
(2009)
J. Theor. Probab.
, vol.22
, pp. 1010-1029
-
-
Herbin, E.1
Merzbach, E.2
-
51
-
-
29244469476
-
Spherical and hyperbolic fractional Brownian motion
-
J. Istas, Spherical and hyperbolic fractional Brownian motion. Electron. Comm. Probab. 10 (2005) 254-262.
-
(2005)
Electron. Comm. Probab.
, vol.10
, pp. 254-262
-
-
Istas, J.1
-
52
-
-
33750067368
-
On fractional stable fields indexed by metric spaces
-
J. Istas, On fractional stable fields indexed by metric spaces. Electron. Comm. Probab. 11 (2006) 242-251.
-
(2006)
Electron. Comm. Probab.
, vol.11
, pp. 242-251
-
-
Istas, J.1
-
53
-
-
33745208472
-
Karhunen-Loeve expansion of spherical fractional Brownian motions
-
J. Istas, Karhunen-Loeve expansion of spherical fractional Brownian motions. Stat. Probab. Lett. 76 (2006) 1578-1583.
-
(2006)
Stat. Probab. Lett.
, vol.76
, pp. 1578-1583
-
-
Istas, J.1
-
54
-
-
33847385134
-
Quadratic variations of spherical fractional Brownian motions
-
J. Istas, Quadratic variations of spherical fractional Brownian motions, Stoc. Proc. Appl. 117 (2007) 476-486.
-
(2007)
Stoc. Proc. Appl.
, vol.117
, pp. 476-486
-
-
Istas, J.1
-
55
-
-
33749532999
-
Identifying the anisotropical function of a d-dimensional Gaussian self-similar process with stationary increments
-
J. Istas, Identifying the anisotropical function of a d-dimensional Gaussian self-similar process with stationary increments. Stat. Inf. Stoc. Proc. 10-11 (2007) 97-106.
-
(2007)
Stat. Inf. Stoc. Proc.
, vol.10-11
, pp. 97-106
-
-
Istas, J.1
-
57
-
-
0040826627
-
Variations quadratiques et estimation de l’exposant de Holder local d’un processus gaussien
-
J. Istas and G. Lang, Variations quadratiques et estimation de l’exposant de Holder local d’un processus gaussien. C. R. Acad. Sci. Sér.I Paris 319 (1994) 201-206.
-
(1994)
C. R. Acad. Sci. Sér.I Paris
, vol.319
, pp. 201-206
-
-
Istas, J.1
Lang, G.2
-
58
-
-
0031521238
-
Quadratic variations and estimation of the Holder index of a Gaussian process
-
J. Istas and G. Lang, Quadratic variations and estimation of the Holder index of a Gaussian process. Ann. Inst. Henri Poincare 33 (1997) 407-436.
-
(1997)
Ann. Inst. Henri Poincare
, vol.33
, pp. 407-436
-
-
Istas, J.1
Lang, G.2
-
59
-
-
14244255625
-
Estimating the fractal dimension of a locally self-similar Gaussian process using increments
-
J. Kent and A. Wood, Estimating the fractal dimension of a locally self-similar Gaussian process using increments. J. Roy. Statist. Soc. B 59 (1997) 679-700.
-
(1997)
J. Roy. Statist. Soc. B
, vol.59
, pp. 679-700
-
-
Kent, J.1
Wood, A.2
-
60
-
-
0003180011
-
Schoenberg’s problem on positive definite functions
-
A. Koldobsky, Schoenberg’s problem on positive definite functions. Algebra Anal. 3 (1991) 78-85.
-
(1991)
Algebra Anal
, vol.3
, pp. 78-85
-
-
Koldobsky, A.1
-
61
-
-
0038930638
-
A short proof of Schoenberg’s conjecture on positive definite functions
-
A. Koldobsky and Y. Lonke, A short proof of Schoenberg’s conjecture on positive definite functions. Bull. Lond. Math. Soc. (1999) 693-699.
-
(1999)
Bull. Lond. Math. Soc
, pp. 693-699
-
-
Koldobsky, A.1
Lonke, Y.2
-
62
-
-
0001187166
-
Wienersche Spiralen und einige andere interessante Kurven im Hilbertsche Raum (German)
-
A. Kolmogorov, Wienersche Spiralen und einige andere interessante Kurven im Hilbertsche Raum (German). C. R. (Dokl.) Acad. Sci. URSS 26 (1940) 115-118.
-
(1940)
C. R. (Dokl.) Acad. Sci. URSS
, vol.26
, pp. 115-118
-
-
Kolmogorov, A.1
-
63
-
-
2342547099
-
Real harmonizable multifractional Levy motions
-
C. Lacaux, Real harmonizable multifractional Levy motions. Ann. Inst. Henri Poincaré 40 (2004) 259-277.
-
(2004)
Ann. Inst. Henri Poincaré
, vol.40
, pp. 259-277
-
-
Lacaux, C.1
-
64
-
-
33644924994
-
Semi-parametric estimation of the Holder exponent of a stationary Gaussian process with minimax rates
-
G. Lang and F. Roueff, Semi-parametric estimation of the Holder exponent of a stationary Gaussian process with minimax rates. Stat. Inf. Stoc. Proc. 4-3 (2001) 283-306.
-
(2001)
Stat. Inf. Stoc. Proc.
, vol.4
, Issue.3
, pp. 283-306
-
-
Lang, G.1
Roueff, F.2
-
66
-
-
0002573194
-
Fractional Brownian fields as integrals of white noise
-
T. Lindstrom, Fractional Brownian fields as integrals of white noise. Bull. Lond. Math. Soc. 25 (1993) 83-88.
-
(1993)
Bull. Lond. Math. Soc.
, vol.25
, pp. 83-88
-
-
Lindstrom, T.1
-
67
-
-
84988050333
-
A remark on self-similar processes with stationary increments
-
M. Maejima, A remark on self-similar processes with stationary increments. Can. J. Stat. 14 (1986) 81-82.
-
(1986)
Can. J. Stat.
, vol.14
, pp. 81-82
-
-
Maejima, M.1
-
68
-
-
0000501589
-
Fractional Brownian motions, fractional noises and applications
-
B.B. Mandelbrot and J.W. Van Ness, Fractional Brownian motions, fractional noises and applications, SIAM Rev. 10 (1968) 422-437.
-
(1968)
SIAM Rev
, vol.10
, pp. 422-437
-
-
Mandelbrot, B.B.1
Van Ness, J.W.2
-
70
-
-
0003439973
-
-
Graduate Texts in Mathematics, Springer
-
P. Petersen, Riemannian Geometry. Graduate Texts in Mathematics, Springer (1998).
-
(1998)
Riemannian Geometry
-
-
Petersen, P.1
-
71
-
-
7544240161
-
Testing (Non-)existence of input-output relationships by estimating fractal dimensions
-
E. Rafajlowicz, Testing (non-)existence of input-output relationships by estimating fractal dimensions. IEEE Trans. Signal Process. 52 (2004) 3151-3159.
-
(2004)
IEEE Trans. Signal Process.
, vol.52
, pp. 3151-3159
-
-
Rafajlowicz, E.1
-
72
-
-
25444484090
-
Crofton formulae and geodesic distance in hyperbolic spaces
-
G. Robertson, Crofton formulae and geodesic distance in hyperbolic spaces. J. Lie Theory 8 (1998) 163-172.
-
(1998)
J. Lie Theory
, vol.8
, pp. 163-172
-
-
Robertson, G.1
-
73
-
-
0032340726
-
Negative definite kernels and a dynamical characterization of property T for countable groups
-
G. Robertson and T. Steger, Negative definite kernels and a dynamical characterization of property T for countable groups. Ergod. Theory Dyn. Syst. 18 (1998) 247-253.
-
(1998)
Ergod. Theory Dyn. Syst.
, vol.18
, pp. 247-253
-
-
Robertson, G.1
Steger, T.2
-
77
-
-
0001743201
-
Metric spaces and positive definite functions
-
I. Schonberg, Metric spaces and positive definite functions. Ann. Math. 39 (1938) 811-841.
-
(1938)
Ann. Math.
, vol.39
, pp. 811-841
-
-
Schonberg, I.1
-
78
-
-
0002320656
-
Spherical harmonics
-
R. Seeley, Spherical harmonics. Am. Math. Mon. 73 (1966) 115-121.
-
(1966)
Am. Math. Mon.
, vol.73
, pp. 115-121
-
-
Seeley, R.1
-
79
-
-
13344295054
-
Stochastic properties of the linear multifractional stable motion
-
S. Stoev and M. Taqqu, Stochastic properties of the linear multifractional stable motion. Adv. Appl. Prob. 36 (2004) 1085-1115.
-
(2004)
Adv. Appl. Prob.
, vol.36
, pp. 1085-1115
-
-
Stoev, S.1
Taqqu, M.2
-
80
-
-
0003217929
-
Orthogonal Polynomials
-
4th edition, Providence, RI
-
G. Szego, Orthogonal Polynomials, 4th edition, in Amer. Math. Soc. Providence, RI (1975).
-
(1975)
Amer. Math. Soc.
-
-
Szego, G.1
-
81
-
-
84972525404
-
Integral-geometric construction of self-similar stable processes
-
S. Takenaka, Integral-geometric construction of self-similar stable processes. Nagoya Math. J. 123 (1991) 1-12.
-
(1991)
Nagoya Math. J.
, vol.123
, pp. 1-12
-
-
Takenaka, S.1
-
82
-
-
84972497957
-
Brownian motion parametrized with metric space of constant curvature
-
S. Takenaka, I. Kubo and H. Urakawa, Brownian motion parametrized with metric space of constant curvature. Nagoya Math. J. 82 (1981) 131-140.
-
(1981)
Nagoya Math. J.
, vol.82
, pp. 131-140
-
-
Takenaka, S.1
Kubo, I.2
Urakawa, H.3
-
83
-
-
0039178948
-
Les representations uniformement bornees associees a un arbre reel
-
A. Valette, Les representations uniformement bornees associees a un arbre reel. Bull. Soc. Math. Belgique 42 (1990) 747-760.
-
(1990)
Bull. Soc. Math. Belgique
, vol.42
, pp. 747-760
-
-
Valette, A.1
-
84
-
-
0000162483
-
Two-point homogeneous spaces
-
H. Wang, Two-point homogeneous spaces. Ann. Math. 2 (1952) 177-191.
-
(1952)
Ann. Math.
, vol.2
, pp. 177-191
-
-
Wang, H.1
-
85
-
-
0000510857
-
Some classes of random fields in n-dimensional space, related to stationary random processes
-
A. Yaglom, Some classes of random fields in n-dimensional space, related to stationary random processes. Theory Probab. Appl. 2 (1957) 273-320.
-
(1957)
Theory Probab. Appl.
, vol.2
, pp. 273-320
-
-
Yaglom, A.1
-
86
-
-
84996144594
-
-
North Holland Publishing Co
-
A. Zaanen, Linear Anal. North Holland Publishing Co (1960).
-
(1960)
Linear Anal
-
-
Zaanen, A.1
|