R. J. Adler-]-r, D. Adler, R. H. Monrad, R. Scissors, and . Wilson, Hausdorff Dimension and Gaussian Fields, Institute of mathematical statistics, pp.145-151, 1977.
DOI : 10.1214/aop/1176995900

]. R. Adler and J. E. Taylor, Random fields and geometry Yoshida, H ? C 1 Maps and elliptic SPDEs with polynomial and exponential perturbations of Nelson's Euclidean free field, J. Funct. Anal, issue.5 2, pp.196-265, 2002.

K. S. Alexander, Probability Inequalities for Empirical Processes and a Law of the Iterated Logarithm, The Annals of Probability, vol.12, issue.4, pp.1041-1067, 1984.
DOI : 10.1214/aop/1176993141

T. W. Anderson, Sample Moduli for Set-Indexed Gaussian Processes The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities, Proc. Am, pp.598-611, 1955.

A. Araujo and E. Giné, On tails and domains of attraction of stable measures in Banach spaces, Transactions of the American Mathematical Society, vol.248, issue.1, pp.105-119, 1979.
DOI : 10.1090/S0002-9947-1979-0521695-1

A. Ayache, N. Shieh, and Y. Xiao, Multiparameter multifractional Brownian motion: Local nondeterminism and joint continuity of the local times, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.47, issue.4, pp.47-1029, 2011.
DOI : 10.1214/10-AIHP408

A. Ayache and M. S. Taqqu, Multifractional processes with random exponent, Publicacions Matem??tiques, vol.49, pp.459-486, 2005.
DOI : 10.5565/PUBLMAT_49205_11

R. M. Balan, Set-Markov processes, 2001.

R. M. Balan and B. G. Ivanoff, A strong Markov property for set-indexed processes, Statistics & Probability Letters, vol.53, issue.2, pp.553-588, 2002.
DOI : 10.1016/S0167-7152(01)00091-8

P. Balança, An Increment-Type Set-Indexed Markov Property, Journal of Theoretical Probability, vol.47, issue.3???41, 2012.
DOI : 10.1007/s10959-014-0555-y

P. Balança and E. Herbin, 2-Microlocal Analysis of Martingales and Stochastic Integrals, Stochastic Process, Appl, vol.122, issue.6, pp.2346-2382, 2012.

D. Baraka, T. S. Mountford, and Y. Xiao, H??lder properties of local times for fractional Brownian motions, Metrika, vol.15, issue.2-3, pp.125-152, 2008.
DOI : 10.1007/s00184-008-0211-6

R. F. Bass and R. Pyke, The existence of set-indexed L???vy processes, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.12, issue.2, pp.157-172, 1984.
DOI : 10.1007/BF00531526

A. Benassi, S. Jaffard, and D. Roux, Elliptic gaussian random processes, Revista Matem??tica Iberoamericana, vol.13, issue.1, pp.19-90, 1997.
DOI : 10.4171/RMI/217

S. M. Berman, Gaussian Processes with Stationary Increments: Local Times and Sample Function Properties, The Annals of Mathematical Statistics, vol.41, issue.4, pp.1260-1272, 1970.
DOI : 10.1214/aoms/1177696901

L. Beznea, A. Cornea, and M. Röckner, Potential theory of infinite dimensional L??vy processes, Journal of Functional Analysis, vol.261, issue.10, pp.2845-2876, 2011.
DOI : 10.1016/j.jfa.2011.07.016

C. Borell, Gaussian radon measures on locally convex spaces., MATHEMATICA SCANDINAVICA, vol.38, pp.265-284, 1976.
DOI : 10.7146/math.scand.a-11634

URL : http://www.digizeitschriften.de/download/PPN35397434X_0038/PPN35397434X_0038___log26.pdf

J. Breton, I. Nourdin, and G. Peccati, Exact confidence intervals for the Hurst parameter of a fractional Brownian motion, Electronic Journal of Statistics, vol.3, issue.0, pp.416-425, 2009.
DOI : 10.1214/09-EJS366

URL : https://hal.archives-ouvertes.fr/hal-00356718

R. Cairoli, Un théorème de convergence pour martingales à indices multiples, CR Acad. Sci. Paris Sér. AB, vol.269, pp.587-589, 1969.

R. Cairoli and J. B. Walsh, Stochastic integrals in the plane, Acta Mathematica, vol.134, issue.0, pp.111-183, 1975.
DOI : 10.1007/BF02392100

R. Carmona, Tensor product of Gaussian measures, Vector Space Measures and Applications I, pp.96-124, 1978.

L. Chen and D. Jakobson, Gaussian Free Fields and KPZ Relation in 4, 2013.

N. N. Chentsov, Lévy Brownian Motion for Several Parameters and Generalized White Noise, Theory Probab, Appl, vol.2, issue.2, pp.265-266, 1957.

K. L. Chung, On the maximum partial sums of sequences of independent random variables, Transactions of the American Mathematical Society, vol.64, issue.2, pp.205-233, 1948.
DOI : 10.1090/S0002-9947-1948-0026274-0

E. Csáki, A relation between Chung's and Strassen's laws of the iterated logarithm, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.3, issue.3, pp.287-301, 1980.
DOI : 10.1007/BF00534347

R. C. Dalang, Extending martingale measure stochastic integral with applications to spatially homogeneous SPDEs, Electron, J. Probab, vol.4, pp.1-29, 1999.

R. C. Dalang, E. Nualart, D. Khoshnevisan, D. Wu, and Y. Xiao, Critical Brownian sheet does not have double points, The Annals of Probability, vol.40, issue.4, pp.1-32, 2012.
DOI : 10.1214/11-AOP665

URL : http://arxiv.org/abs/1009.0235

R. C. Dalang and J. B. Walsh, The Sharp Markov Property of Levy Sheets, The Annals of Probability, vol.20, issue.2, pp.591-626, 1992.
DOI : 10.1214/aop/1176989793

A. De-acosta, Stable Measures and Seminorms, The Annals of Probability, vol.3, issue.5, pp.865-875, 1975.
DOI : 10.1214/aop/1176996273

L. Decreusefond and A. S. , Stochastic Analysis of the Fractional Brownian Motion, Potential Anal, pp.177-214, 1999.

P. Deheuvels and D. M. Mason, Random fractal functional laws of the iterated logarithm, Studia Scientiarum Mathematicarum Hungarica, vol.34, issue.1, pp.89-106, 1998.

V. Dobric and F. M. Ojeda, Fractional Brownian fields, duality, and martingales, IMS Lecture Notes-Monograph series. High dimensional probability, pp.51-77, 2006.

J. L. Doob, Stochastic processes, 1953.

R. M. Dudley, The sizes of compact subsets of Hilbert space and continuity of Gaussian processes, Journal of Functional Analysis, vol.1, issue.3, pp.290-330, 1967.
DOI : 10.1016/0022-1236(67)90017-1

K. Falconer, Fractal geometry: Mathematical Foundations and Applications, 2003.
DOI : 10.1002/0470013850

K. J. Falconer, Tangent Fields and the Local Structure of Random Fields, Journal of Theoretical Probability, vol.15, issue.3, pp.731-750, 2002.
DOI : 10.1023/A:1016276016983

A. Garsia, E. Rodemich, and H. Rumsey, A Real Variable Lemma and the Continuity of Paths of Some Gaussian Processes, Indiana University Mathematics Journal, vol.20, issue.6, pp.565-578, 1970.
DOI : 10.1512/iumj.1971.20.20046

I. M. Gel-'fand and N. Y. , Applications of harmonic analysis, Vilenkin, Generalized Functions, vol.4, 1964.

I. I. Gikhman and A. V. Skorokhod, Introduction to the theory of random processes, W.B. Saunders Company, 1969.

V. Goodman, Characteristics of Normal Samples, The Annals of Probability, vol.16, issue.3, pp.1281-1290, 1988.
DOI : 10.1214/aop/1176991690

V. Goodman and J. Kuelbs, Rates of clustering for some Gaussian self-similar processes, Probability Theory and Related Fields, vol.68, issue.1, pp.47-75, 1991.
DOI : 10.1007/BF01193582

L. Gross, Abstract Wiener spaces, Fifth Berkeley symposium on Math. Statist. and Prob, pp.31-42, 1967.

E. Herbin, From $N$ Parameter Fractional Brownian Motions to $N$ Parameter Multifractional Brownian Motions, Rocky Mountain Journal of Mathematics, vol.36, issue.4, pp.1249-1284, 2006.
DOI : 10.1216/rmjm/1181069415

URL : https://hal.archives-ouvertes.fr/hal-00539236

E. Herbin, B. Arras, and G. Barruel, From almost sure local regularity to almost sure Hausdorff dimension for Gaussian fields, ESAIM: Probability and Statistics, vol.18, 2013.
DOI : 10.1051/ps/2013044

URL : https://hal.archives-ouvertes.fr/hal-00862543

E. Herbin and J. Lévy, Stochastic 2-microlocal analysis, Stochastic Process, Appl, vol.119, issue.7, pp.2277-2311, 2009.

E. Herbin and E. Merzbach, A Set-indexed Fractional Brownian Motion, Journal of Theoretical Probability, vol.122, issue.2, pp.337-364, 2006.
DOI : 10.1007/s10959-006-0019-0

URL : https://hal.archives-ouvertes.fr/hal-00652069

E. Herbin and A. Richard, Local Hölder regularity of set-indexed processes, Preprint, 2012.

E. Herbin and Y. Xiao, Sample paths properties of the set-indexed fractional Brownian motion, 2014.

H. E. Hurst, Long-term storage capacity of reservoirs, Trans. Amer. Soc. Civil Engineers, vol.116, pp.770-808, 1951.

K. Ito, Stationary random distributions, Memoirs of the College of Science, University of Kyoto. Series A: Mathematics, vol.28, issue.3, pp.209-223, 1954.
DOI : 10.1215/kjm/1250777359

G. Ivanoff, Set-Indexed Processes: Distributions and Weak Convergence, Lecture Notes in Mathematics, vol.1802, pp.85-125, 2003.
DOI : 10.1007/978-3-540-36259-3_3

G. Ivanoff and E. Merzbach, Set-indexed Markov processes, Stochastic models, Conference proceedings of the CMS, pp.217-232, 1998.

G. Ivanoff and P. Sawyer, Local time for processes indexed by a partially ordered set, Statistics & Probability Letters, vol.61, issue.1, pp.61-62, 2003.
DOI : 10.1016/S0167-7152(02)00161-X

M. Jolis, On the Wiener integral with respect to the fractional Brownian motion on an interval, Journal of Mathematical Analysis and Applications, vol.330, issue.2, pp.1115-1127, 2007.
DOI : 10.1016/j.jmaa.2006.07.100

M. Jolis and N. Viles, Continuity in the Hurst parameter of the law of the symmetric integral with respect to the fractional Brownian motion, Stochastic Process, Appl, vol.120, issue.9, pp.1651-1679, 2010.

O. Kallenberg, Foundations of modern probability, 2002.
DOI : 10.1007/978-1-4757-4015-8

A. Kamont, On the fractional anisotropic Wiener field, Probab, Math. Stat, vol.16, issue.1, pp.85-98, 1995.

D. Khoshnevisan, Multiparameter Processes: an introduction to random fields, 2002.
DOI : 10.1007/b97363

D. Khoshnevisan, Y. Peres, and Y. Xiao, Limsup Random Fractals, Electronic Journal of Probability, vol.5, issue.0, pp.1-24, 2000.
DOI : 10.1214/EJP.v5-60

D. Khoshnevisan and Z. Shi, Fast sets and points for fractional Brownian motion, pp.393-416, 2000.
DOI : 10.1017/S0305004100066160

D. Khoshnevisan and Y. Xiao, L??vy processes: Capacity and Hausdorff dimension, The Annals of Probability, vol.33, issue.3, pp.841-878, 2005.
DOI : 10.1214/009117904000001026

T. Kitagawa, ANALYSIS OF VARIANCE APPLIED TO FUNCTION SPACES, Memoirs of the Faculty of Science, Kyushu University. Series A, Mathematics, vol.6, issue.1, pp.41-53, 1951.
DOI : 10.2206/kyushumfs.6.41

A. N. Kolmogorov, Wienersche Spiralen und einige andere interessante Kurven im Hilbertschen Raum, CR (Dokl.) Acad. Sci. URSS, vol.26, pp.115-118, 1940.

J. Kuelbs, A representation theorem for symmetric stable processes and stable measures on H, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.24, issue.4, pp.259-271, 1973.
DOI : 10.1007/BF00534891

J. Kuelbs and W. V. Li, Metric Entropy and the Small Ball Problem for Gaussian Measures, Journal of Functional Analysis, vol.116, issue.1, pp.133-157, 1993.
DOI : 10.1006/jfan.1993.1107

J. Kuelbs, W. V. Li, and M. Talagrand, Lim Inf Results for Gaussian Samples and Chung's Functional LIL, The Annals of Probability, vol.22, issue.4, pp.1879-1903, 1994.
DOI : 10.1214/aop/1176988488

H. H. Kuo, Gaussian measures in Banach spaces, 1975.

G. F. Lawler and F. J. Viklund, Optimal Hölder exponent for the SLE path, Duke Math, J, vol.159, issue.3, pp.351-383, 2011.

J. Lebovits, J. L. Véhel, and E. Herbin, Stochastic integration with respect to multifractional Brownian motion via tangent fractional Brownian motions, Stochastic Process, Appl, 2013.

N. Leonenko, M. D. Ruiz-medina, M. S. Taqqu, and F. Elliptic, Hyperbolic and Parabolic Random Fields, Electron, J. Probab, vol.16, pp.1134-1172, 2011.

P. Lévy, Exemples de processus doubles de Markoff, CR Acad. Sci. Paris, vol.226, pp.307-308

W. V. Li and W. Linde, Approximation, metric entropy and small ball estimates for Gaussian measures, Ann. Probab, vol.27, issue.3, pp.1556-1578, 1999.

M. Lifshits, W. Linde, and Z. Shi, Small deviations of Riemann-Liouville processes in L q norms with respect to fractal measures, Proc. London Math. Soc. 92, pp.224-250, 2006.

M. Loève, Probability Theory I, 1977.

N. Luan and Y. Xiao, Chung???s law of the iterated logarithm for anisotropic Gaussian random fields, Statistics & Probability Letters, vol.80, issue.23-24, pp.23-24, 2010.
DOI : 10.1016/j.spl.2010.08.016

B. B. Mandelbrot and J. W. , Fractional Brownian Motions, Fractional Noises and Applications, SIAM Review, vol.10, issue.4, pp.422-437, 1968.
DOI : 10.1137/1010093

M. B. Marcus, Hölder conditions for Gaussian processes with stationary increments, Trans. Amer. Math. Soc, vol.134, issue.1, pp.29-52, 1968.

D. M. Mason and Z. Shi, Small Deviations for Some Multi-Parameter Gaussian Processes, Journal of Theoretical Probability, vol.14, issue.1, pp.213-239, 2001.
DOI : 10.1023/A:1007833401562

H. P. Mckean, Brownian Motion with a Several-Dimensional Time, Theory Probab, Appl, vol.8, issue.4, pp.335-354, 1963.

M. M. Meerschaert, W. Wang, and Y. Xiao, Fernique-type inequalities and moduli of continuity for anisotropic Gaussian random fields, Transactions of the American Mathematical Society, vol.365, issue.2, pp.1081-1107, 2012.
DOI : 10.1090/S0002-9947-2012-05678-9

E. Merzbach and D. Nualart, Markov Properties for Point Processes on the Plane, The Annals of Probability, vol.18, issue.1, pp.342-358, 1990.
DOI : 10.1214/aop/1176990952

R. A. Minlos, Generalized random processes and their extension to a measure, Selected Translations in mathematical statistics and probability 3, 1959.

D. Monrad and H. Rootzén, Small values of Gaussian processes and functional laws of the iterated logarithm, Probability Theory and Related Fields, vol.3, issue.2, pp.173-192, 1995.
DOI : 10.1007/BF01375823

E. Nelson, Construction of quantum fields from Markoff fields, Journal of Functional Analysis, vol.12, issue.1, pp.97-112, 1973.
DOI : 10.1016/0022-1236(73)90091-8

I. Nourdin, Selected aspects of fractional Brownian motion, 2013.
DOI : 10.1007/978-88-470-2823-4

URL : https://hal.archives-ouvertes.fr/hal-01314412

D. Nualart, The Malliavin calculus and related topics, 2006.
DOI : 10.1007/978-1-4757-2437-0

D. Nualart and S. Tindel, Quasilinear stochastic elliptic equations with reflection, Stochastic Process, Appl, vol.57, issue.1, pp.73-82, 1995.

S. Orey, Growth rate of certain Gaussian processes, Proc. Sixth Berkeley Symp. Math. Statist. Probab, pp.443-451, 1972.

S. Orey and W. E. Pruitt, Sample Functions of the $N$-Parameter Wiener Process, The Annals of Probability, vol.1, issue.1, pp.138-163, 1973.
DOI : 10.1214/aop/1176997030

S. Orey and S. J. Taylor, How Often on a Brownian Path Does the Law of Iterated Logarithm Fail?, Proc. London Math, pp.174-192, 1974.
DOI : 10.1112/plms/s3-28.1.174

M. Ossiander and R. Pyke, Lévy's Brownian motion as a set-indexed process and a related central limit theorem, Stochastic Process, Appl, vol.21, issue.1, pp.133-145, 1985.

R. Peltier and J. L. Véhel, Multifractional Brownian motion: definition and preliminary results, INRIA technical report, p.2645, 1995.
URL : https://hal.archives-ouvertes.fr/inria-00074045

L. D. Pitt, Local times for Gaussian vector fields, Indiana Univ, Math. J, vol.27, pp.309-330, 1978.

R. Pyke, Asymptotic results for empirical and partial-sum processes: A review, Canadian Journal of Statistics, vol.1, issue.4, pp.241-264, 1984.
DOI : 10.2307/3314809

M. Reed and B. Simon, I: Functional analysis, Methods of Modern Mathematical Physics, 1980.

A. Richard, Some Singular Sample Path Properties of a Multiparameter Fractional Brownian Motion, Journal of Theoretical Probability, vol.2, issue.3, 2014.
DOI : 10.1007/s10959-016-0694-4

URL : https://hal.archives-ouvertes.fr/hal-01075245

Y. A. Rozanov, Spectral Analysis of Abstract Functions, Theory Probab, Appl, vol.4, issue.3, pp.271-287, 1959.

W. Rudin, Real and complex analysis, Series in higher mathematics, 1987.

F. Russo, Etude de la propriété de Markov étroite en relation avec les processus planaires à accroissements indépendants, Séminaire de probabilités XVIII, pp.353-378, 1984.

R. A. Ryan, Introduction to Tensor Products of Banach Spaces, 2002.
DOI : 10.1007/978-1-4471-3903-4

S. G. Samko and A. A. , Kilbas, and O. I. Marichev, Fractional integrals and derivatives: Theory and applications, Gordon and Breach Science, 1993.

K. Sato, Lévy processes and infinitely divisible distributions, Cambridge Studies in Advanced Mathematics, 1999.

L. Schwartz, La fonction aléatoire du mouvement brownien, Séminaire Bourbaki, vol.4, pp.327-349, 1958.

I. E. Segal, Abstract Probability Spaces and a Theorem of Kolmogoroff, American Journal of Mathematics, vol.76, issue.3, pp.721-732, 1954.
DOI : 10.2307/2372714

Q. Shao and D. Wang, Small ball probabilities of Gaussian fields, Probability Theory and Related Fields, vol.22, issue.4, pp.511-517, 1995.
DOI : 10.1007/BF01198847

S. Sheffield, Gaussian free fields for mathematicians, Probab. Theory Related Fields 139, pp.521-541, 2007.

S. Stoev and M. S. Taqqu, How rich is the class of multifractional Brownian motions?, Stochastic Process, Appl, vol.116, issue.2, pp.200-221, 2006.

V. Strassen, An invariance principle for the law of the iterated logarithm, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.104, issue.3, pp.211-226, 1964.
DOI : 10.1007/BF00534910

D. W. Stroock, Probability Theory: An Analytic View, 2010.
DOI : 10.1017/CBO9780511974243

S. Takenaka, Representation of Euclidean Random Field, Nagoya Mathematical Journal, vol.3, pp.19-31
DOI : 10.1016/0304-4149(85)90382-5

S. Takenaka, I. Kubo, and H. Urakawa, Brownian motion parametrized with metric space of constant curvature, Nagoya Mathematical Journal, vol.221, pp.131-140, 1981.
DOI : 10.1017/S0027763000019322

M. Talagrand, Regularity of gaussian processes, New Gaussian estimates for enlarged balls, pp.99-149, 1987.
DOI : 10.1007/BF02392556

S. J. Taylor, The measure theory of random fractals, Mathematical Proceedings of the Cambridge Philosophical Society, vol.30, issue.02, pp.383-406, 1986.
DOI : 10.1215/S0012-7094-55-02223-7

C. A. Tudor and Y. Xiao, Sample path properties of bifractional Brownian motion, Bernoulli, vol.13, issue.4, pp.1023-1052, 2007.
DOI : 10.3150/07-BEJ6110

URL : https://hal.archives-ouvertes.fr/hal-00083060

J. B. Walsh, An introduction to stochastic partial differential equations, Lecture Notes in Mathematics, vol.1180, pp.265-439, 1986.
DOI : 10.1007/BFb0074920

N. Wiener, Differential-Space, Journal of Mathematics and Physics, vol.2, issue.1-4, pp.131-174, 1923.
DOI : 10.1002/sapm192321131

E. Wong and M. Zakai, Martingales and stochastic integrals for processes with a multidimensional parameter, Probab. Theory Related Fields, vol.29, issue.2, pp.109-122, 1974.

Y. Xiao, Hausdorff measure of the sample paths of Gaussian random fields, Osaka J. Math, vol.33, pp.895-913, 1996.

A. M. Yaglom, Some Classes of Random Fields in n -Dimensional Space, Related to Stationary Random Processes, Theory Probab, Appl, vol.2, issue.3, pp.273-320, 1957.

J. A. Yan, Generalizations of Gross' and Minlos' theorems, Séminaire de probabilités XXIII, pp.395-404, 1989.