R. Adler, An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes processes.L e c t u r eN o t e s -M o n o g r a p h sS e r i e s .I n s t i t

E. Alos, O. Mazet, and D. Nualart, Stochastic calculus with respect to Gaussian processes, Annals of Probability, vol.9, issue.2 2

G. Torben, T. Andersen, F. X. Bollerslev, H. Diebold, and . Ebens, The distribution of realized stock return volatility, Journal of Financial Economics

A. Ayache, S. Cohen, and J. Lévy, The covariance structure of multifractional Brownian motion, with application to long-range dependence (extended version), ICASSP,R e f e r e e d Conference Contribution, 2000.

V. Bally, An elementary introduction to Malliavin calculus. rapport de recherche no 4718, 2003.
URL : https://hal.archives-ouvertes.fr/inria-00071868

A. Benassi, S. Jaffard, and D. Roux, Elliptic gaussian random processes, Revista Matem??tica Iberoamericana, vol.3, issue.1 1
DOI : 10.4171/RMI/217

C. Bender, An It?? formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter, Stochastic Processes and their Applications
DOI : 10.1016/S0304-4149(02)00212-0

C. Bender, An S -transform approach to integration with respect to a fractional Brownian motion, Bernoulli, vol.9, issue.6, pp.9-14
DOI : 10.3150/bj/1072215197

C. Bender, T. Sottinen, and E. Valkeila, Arbitrage with fractional Brownian motion? Theory Stoch, Process

F. Biagini, A. Sulem, B. Øksendal, and N. N. Wallner, An introduction to white-noise theory and Malliavin calculus for fractional Brownian motion, Proc. Royal Society, special issue on stochastic analysis and applications, 0372.
DOI : 10.1098/rspa.2003.1246

F. Biagini, Y. Hu, B. Øksendal, and T. Zhang, Stochastic calculus for fractional Brownian motion and applications
DOI : 10.1007/978-1-84628-797-8

F. Biagini, B. Øksendal, A. Sulem, and N. Wallner, An introduction to white-noise theory and Malliavin calculus for fractional Brownian motion, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.460, issue.2041
DOI : 10.1098/rspa.2003.1246
URL : https://www.duo.uio.no/bitstream/10852/10633/1/pm02-03.pdf

F. Biagini, B. Øksendal, A. Sulem, and N. Wallner, An introduction to white-noise theory and Malliavin calculus for fractional Brownian motion, Proc. R. Soc. Lond. Ser. A Math. Phys
DOI : 10.1098/rspa.2003.1246
URL : https://www.duo.uio.no/bitstream/10852/10633/1/pm02-03.pdf

S. Bianchi, PATHWISE IDENTIFICATION OF THE MEMORY FUNCTION OF MULTIFRACTIONAL BROWNIAN MOTION WITH APPLICATION TO FINANCE, International Journal of Theoretical and Applied Finance, vol.08, issue.02
DOI : 10.1142/S0219024905002937

P. Billingsley, Convergence of probability measures.W i l e yS e r i e si n P r o b a b i l i t y a n d S t a t i s t i c s : Probability and Statistics, 1999.

T. Björk and H. Hult, A note on Wick products and the fractional Black-Scholes model, Finance Stoch, vol.9, issue.2

B. Boufoussi, M. Dozzi, and R. Marty, Local time and Tanaka formula for a Volterra-type multifractional Gaussian process, Bernoulli, vol.16, issue.4
DOI : 10.3150/10-BEJ261
URL : https://hal.archives-ouvertes.fr/hal-00389740

J. C. Bronski, Asymptotics of Karhunen-Loeve Eigenvalues and Tight Constants for Probability Distributions of Passive Scalar Transport, Communications in mathematical physics, pp.5-6, 2003.
DOI : 10.1007/s00220-003-0835-3

J. Y. Chemin, Analyse harmonique et équation des ondes et de Schrödinger, 2003.

I. M. Chilov and G. E. Gelfand, Les distributions,v o l u m e1

I. M. Chilov and G. E. Gelfand, Les distributions,v o l u m e2

F. Comte, L. Coutin, and É. Renault, Affine fractional stochastic volatility models with application to option pricing, Annals of Finance

F. Comte and É. Renault, Long memory in continuous-time stochastic volatility models, Mathematical Finance, vol.8, issue.4
DOI : 10.1111/1467-9965.00057

S. Corlay, The Nyström method for functional quantization with an application to the fractional Brownian motion

S. Corlay, Some aspects of optimal quantization and applications to finance.P h Dt h e s i s ,U n i v e r s i t é Pierre et Marie Curie, 2011.
URL : https://hal.archives-ouvertes.fr/tel-00626445

S. Corlay and G. Pagès, Abstract, Monte Carlo Methods and Applications, vol.21, issue.1, 2010.
DOI : 10.1515/mcma-2014-0010

L. Coutin, An Introduction to (Stochastic) Calculus with Respect to Fractional Brownian Motion
DOI : 10.1007/978-3-540-71189-6_1
URL : https://hal.archives-ouvertes.fr/hal-00635584

G. Da, P. , and J. Zabczyk, Stochastic equations in infinite dimensions,v o l u m e4 4o f Encyclopedia of Mathematics and its Applications.C a m b r i d g eU n i v e r s i t yP r e s s ,C a m b r i d g e, pp.9-9

L. Decreusefond and A. S. , Stochastic analysis of the fractional Brownian motion. Potential Anal, pp.0-1

P. Deheuvels and G. V. Martynov, A Karhunen???Loeve decomposition of a Gaussian process generated by independent pairs of exponential random variables, Journal of Functional Analysis, vol.255, issue.9, pp.2363-2394, 2008.
DOI : 10.1016/j.jfa.2008.07.021

A. Echelard, O. Barrière, J. Lévy-véhel, L. Bolc, R. Tadeusiewicz et al., Terrain modelling with multifractional Brownian motion and self-regulating processes, Computer Vision and Graphics. Second International Conference Proceedings, Part I ICCVG,v o l u m e6 3 7 4o fLecture Notes in Computer Science, pp.3-4, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00538907

R. J. Elliott and J. Van-der-hoek, A General Fractional White Noise Theory And Applications To Finance, Mathematical Finance, vol.7, issue.2
DOI : 10.1023/A:1008634027843

K. Falconer and J. L. Véhel, Multifractional, Multistable, and Other Processes with??Prescribed Local Form, Journal of Theoretical Probability, vol.13, issue.2
DOI : 10.1007/s10959-008-0147-9
URL : https://hal.archives-ouvertes.fr/inria-00539033

P. K. Friz and N. B. Victoir, Multidimensional Stochastic Processes as Rough Paths: Theory and Applications .C a m b r i d g eU n i v e r s i t yP r e s s
DOI : 10.1017/CBO9780511845079

S. Graf, H. Luschgy, and G. Pagès, Distortion mismatch in the quantization of probability measures, ESAIM: Probability and Statistics, vol.12
DOI : 10.1051/ps:2007044
URL : https://hal.archives-ouvertes.fr/hal-00019228

E. Herbin, Processus (multi-) fractionnaires à paramètres multidimensionnels et régularité.P h Dt h e s i s, 2004.

E. Herbin, From $N$ Parameter Fractional Brownian Motions to $N$ Parameter Multifractional Brownian Motions, Rocky Mountain Journal of Mathematics, vol.36, issue.4
DOI : 10.1216/rmjm/1181069415
URL : https://hal.archives-ouvertes.fr/hal-00539236

E. Herbin, J. Lebovits, and J. L. Véhel, Stochastic integration with respect to multifractional brownian motion via tangent fractional brownian motion. preprint
URL : https://hal.archives-ouvertes.fr/hal-00653808

E. Herbin and J. Lévy, Stochastic 2 micro-local analysis. Stochastic Processes and their Applications
URL : https://hal.archives-ouvertes.fr/inria-00538965

T. Hida, Brownian Motion.S p r i n g e r -V e r l a g

T. Hida, H. Kuo, J. Potthoff, and L. Streit, White Noise. An infinite dimensional calculus, 1993.

E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups,v o l u m e3 1 . A m e r i c a nM, Society, 1957.

F. Hirsch, B. Roynette, and M. Yor, From an It?? type calculus for Gaussian processes to integrals of log-normal processes increasing in the convex order, Journal of the Mathematical Society of Japan, vol.63, issue.3, pp.887-917, 2011.
DOI : 10.2969/jmsj/06330887

H. Holden, B. Oksendal, J. Ubøe, and T. Zhang, Stochastic Partial Differential Equations, A Modeling, White Noise Functional Approach.S p r i n g e r ,s e c o n de d i t i o n

S. Janson, Gaussian Hilbert spaces.C a m b r i d g eu n i v e r s i t yp r e s s, pp.9-9
DOI : 10.1017/cbo9780511526169

B. Jourdain, Loss of martingality in asset price models with lognormal stochastic volatility

J. Kahane, Some random series of functions,v o l u m e5o fCambridge Studies in Advanced Mathematics.C a m b r i d g eU n i v e r s i t yP r e s s ,C a m b r i d g e ,s e c o n de d i t i o n

A. Kolmogorov, Wienersche Spiralen und einige andere interessante Kurven in Hilbertsche Raum, C. R. (Dokl.) Acad. Sci. URSS

A. N. Kolmogorov, Wienersche spiralen und einige andere interessante kurven im hilbertschen raume

H. H. Kuo, White Noise Distribution Theory, 1996.

J. Lebovits and J. L. Véhel, White noise-based stochastic calculus with respect to multifractional Brownian motion, Stochastics An International Journal of Probability and Stochastic Processes, vol.55, issue.1
DOI : 10.1007/s004400050171
URL : https://hal.archives-ouvertes.fr/inria-00580196

A. Lejay and V. Reutenauer, A variance reduction technique using a quantized Brownian motion as a control variate, The Journal of Computational Finance, vol.16, issue.2
DOI : 10.21314/JCF.2012.242
URL : https://hal.archives-ouvertes.fr/inria-00393749

M. Li, S. C. Lim, B. J. Hu, and H. Feng, Towards Describing Multi-fractality of Traffic Using Local Hurst Function, In Lecture Notes in Computer Science
DOI : 10.1007/978-3-540-72586-2_143

H. Luschgy and G. Pagès, Functional quantization of Gaussian processes, Journal of Functional Analysis, vol.196, issue.2
DOI : 10.1016/S0022-1236(02)00010-1
URL : https://hal.archives-ouvertes.fr/hal-00102159

H. Luschgy and G. Pagès, Sharp asymptotics of the functional quantization problem for Gaussian processes, Annals of Probability, vol.2, issue.2
URL : https://hal.archives-ouvertes.fr/hal-00102159

H. Luschgy and G. Pagès, Functional quantization of a class of Brownian diffusions: A constructive approach, Stochastic Processes and their Applications
DOI : 10.1016/j.spa.2005.09.003
URL : https://hal.archives-ouvertes.fr/hal-00018855

H. Luschgy and G. Pagès, Functional quantization rate and mean regularity of processes with an application to L??vy processes, The Annals of Applied Probability, vol.18, issue.2, pp.4-6
DOI : 10.1214/07-AAP459

B. Mandelbrot and J. W. Van-ness, Fractional Brownian Motions, Fractional Noises and Applications, SIAM Review, vol.10, issue.4, pp.0-4
DOI : 10.1137/1010093

S. Yuliya and . Mishura, Stochastic calculus for fractional Brownian motion and related processes,v o l u m e 1929 of Lecture Notes in Mathematics.S p r i n g e r -V e r l a g

J. Neveu, Processus aléatoires gaussiens Les Presses de l, 1968.

D. Nualart, The Malliavin Calculus and related Topics.S p r i n g e r

D. Nualart, A white noise approach to fractional Brownian motion In Stochastic analysis: classical and quantum,p a g e s1 1 2 ? 1 2 6 .W o r l dS c i .P u b l

G. Pagès and J. Printems, Optimal quadratic quantization for numerics: the Gaussian case, Monte Carlo Methods and Applications, vol.9, issue.2
DOI : 10.1515/156939603322663321

G. Pagès and J. Printems, Functional quantization for numerics with an application to option pricing, Monte Carlo Methods and Applications, vol.11, issue.4
DOI : 10.1515/156939605777438578

R. Peltier and J. Lévy, Multifractional brownian motion, 1995.
URL : https://hal.archives-ouvertes.fr/inria-00074045

D. Pollard, Convergence of stochastic processes.S p r i n g e rS e r i e si nS t a t i s t i c s .S p r i n g e r -V e r l a g, 1984.

J. Pycke, Explicit Karhunen-Lo??ve expansions related to the Green function of the Laplacian, Approximation and Probability
DOI : 10.4064/bc72-0-17

D. Revuz and M. Yor, Continuous martingales and Brownian motion,v olume293ofGrundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences].S p r i n g e r - Verlag, 1999.

L. C. Rogers, Arbitrage with Fractional Brownian Motion, Mathematical Finance, vol.7, issue.1
DOI : 10.1111/1467-9965.00025
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.318.5572

G. Samorodnitsky and M. S. Taqqu, Stable Non-Gaussian Random Processes, Stochastic Models with Infinite Variance

I. J. Schoenberg, Metric spaces and positive definite functions, Transactions of the American Mathematical Society, vol.44, issue.3, pp.522-536, 1938.
DOI : 10.1090/S0002-9947-1938-1501980-0
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.377.3750

S. A. Stoev and M. S. Taqqu, How rich is the class of multifractional Brownian motions? Stochastic Processes and their Applications

M. Talagrand, The generic chaining.S p r i n g e rM o n o g r a p h si nM a t h e m a t i c s .S p r i n g e r -V e r l a g ,B e r l i n

S. Thangavelu, Lectures of Hermite and Laguerre expansions.P r i n c e t o nU n i v e r s i t yP r e s s, pp.9-9

D. V. Widder, Positive Temperatures on an Infinite Rod, Transactions of the American Mathematical Society, vol.55, issue.1
DOI : 10.2307/1990141

M. Zähle, On the Link Between Fractional and Stochastic Calculus, Stochastic dynamics, pp.9-9, 1997.
DOI : 10.1007/0-387-22655-9_13

M. August and . Zapa?a, Jensen's inequality for conditional expectations in Banach spaces. Real Analysis Exchange, pp.5-9