Sharp large deviations for the fractional OrnsteinUhlenbeck process, Theory Probab. Appl, vol.55, issue.4, pp.575-610, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00386239
Sharp large deviations for the Ornstein-Uhlenbeck process, Theory Probab. Appl, vol.46, issue.1, pp.1-19, 2002. ,
URL : https://hal.archives-ouvertes.fr/hal-00386239
Reproducing kernel Hilbert spaces in probability and statistics, 2004. ,
Inference on the Hurst parameter and the variance of diffusions driven by fractional Brownian motion, Lecture Notes in Statistics, vol.216, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00947513
Exact simulation of diffusions, Ann. Appl. Probab, vol.15, issue.4, pp.2422-2444, 2005. ,
Stochastic calculus for fractional Brownian motion and applications, Probability and its Applications, 2008. ,
Asymptotics of Karhunen-Loeve eigenvalues and tight constants for probability distributions of passive scalar transport, Comm. Math. Phys, vol.238, issue.3, pp.563-582, 2003. ,
Small ball constants and tight eigenvalue asymptotics for fractional Brownian motions, J. Theoret. Probab, vol.16, issue.1, pp.87-100, 2003. ,
Mixed gaussian processes: a filtering approach, Ann. Probab, vol.44, issue.4, pp.3032-3075, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01673456
Mixed fractional Brownian motion, Bernoulli, vol.7, issue.6, p.203, 2001. ,
Fractional Ornstein-Uhlenbeck processes, Electron. J. Probab, vol.8, issue.3, p.14, 2003. ,
Exact asymptotics in eigenproblems for fractional Brownian covariance operators, Stochastic Process. Appl, vol.128, issue.6, pp.2007-2059, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01673459
Statistical analysis of the mixed fractional Ornstein-Uhlenbeck process, Teor. Veroyatn. Primen, vol.63, issue.3, pp.500-519, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01740657
Large deviations techniques and applications, of Applications of mathematics, vol.38, 1998. ,
Small deviation probabilities of sums of independent random variables, High dimensional probability, vol.43, pp.59-74, 1996. ,
, Selfsimilar processes. Princeton Series in Applied Mathematics, 2002.
Large deviations in estimation of an OrnsteinUhlenbeck model, J. Appl. Probab, vol.36, issue.1, pp.60-77, 1999. ,
Translated from the Russian, 1990. ,
Integrated Brownian motions and exact L 2 -small balls, Ann. Probab, vol.31, issue.3, pp.1320-1337, 2003. ,
Stochastic analysis and applications, Abel Symp, vol.2, pp.361-382, 2007. ,
Table of integrals, series, and products. Elsevier, With one CD-ROM (Windows, Macintosh and UNIX), 2007. ,
DOI : 10.1115/1.3138251
URL : http://biomechanical.asmedigitalcollection.asme.org/data/journals/jbendy/25673/58_2.pdf
Renormalized self-intersection local time for fractional Brownian motion, Ann. Probab, vol.33, issue.3, p.204, 2005. ,
DOI : 10.1214/009117905000000017
URL : https://doi.org/10.1214/009117905000000017
Simulation and Inference for Stochastic Processes with YUIMA: A Comprehensive R Framework for SDEs and Other Stochastic Processes, 2018. ,
Approximate methods of higher analysis. Translated from the 3rd Russian edition by C, 1958. ,
Perturbation theory for linear operators, Classics in Mathematics, 1995. ,
Optimal linear filtering of general multidimensional Gaussian processes and its application to Laplace transforms of quadratic functionals, J. Appl. Math. Stochastic Anal, vol.14, issue.3, pp.215-226, 2001. ,
The Wiener spiral and some other interesting curves in Hilbert space, Dokl. Akad. Nauk SSSR, vol.26, pp.115-118, 1940. ,
Estimation of the global regularity of a multifractional Brownian motion, Electronic Journal of Statistics, vol.11, issue.1, pp.78-98, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01343318
Testing statistical hypotheses. Springer Texts in Statistics, 2005. ,
Rosenblatt distribution subordinated to Gaussian random fields with long-range dependence, Stoch. Anal. Appl, vol.35, issue.1, pp.144-177, 2017. ,
DOI : 10.1080/07362994.2016.1230723
URL : http://arxiv.org/pdf/1501.02247
Gaussian processes: inequalities, small ball probabilities and applications, Stochastic processes: theory and methods, vol.19, pp.533-597, 2001. ,
DOI : 10.1016/s0169-7161(01)19019-x
Statistics of random processes, Stochastic Modelling and Applied Probability, vol.II ,
Sharp asymptotics of the functional quantization problem for Gaussian processes, Ann. Probab, vol.32, issue.2, p.205, 2004. ,
URL : https://hal.archives-ouvertes.fr/hal-00102159
Optimization of small deviation for mixed fractional brownian motion with trend, Stochastics, 2018. ,
Fractional Brownian motions, fractional noises and applications, SIAM Rev, vol.10, pp.422-437, 1968. ,
DOI : 10.1137/1010093
On an eigenfunction expansion and on fractional Brownian motions, Lett. Nuovo Cimento, vol.33, issue.2, pp.549-550, 1982. ,
DOI : 10.1007/bf02753799
Stochastic calculus for fractional Brownian motion and related processes, Lecture Notes in Mathematics, vol.1929, 2008. ,
DOI : 10.1007/978-3-540-75873-0
Boundary problems of function theory and their application to mathematical physics, Translated from the second (1946) Russian edition and with a preface by, 1992. ,
Exact L 2 -small ball behavior of integrated Gaussian processes and spectral asymptotics of boundary value problems, Probab. Theory Related Fields, vol.129, issue.4, pp.469-494, 2004. ,
Logarithmic asymptotics of small deviations in the L 2 -norm for some fractional Gaussian processes, Teor. Veroyatn. Primen, vol.49, issue.4, pp.695-711, 2004. ,
On small deviation asymptotics in L 2 of some mixed Gaussian processes, Mathematics, vol.6, issue.4, p.55, 2018. ,
Exact L 2 -small ball asymptotics of Gaussian processes and the spectrum of boundary-value problems, J. Theoret. Probab, vol.22, issue.3, pp.640-665, 2009. ,
On a family of transformations of Gaussian random functions, Teor. Veroyatn. Primen, vol.54, issue.2, pp.209-225, 2009. ,
Rosenbaum Fractional Brownian motion with zero Hurst parameter: a rough volatility viewpoint, Electronic Communications in Probability, vol.23, 2018. ,
Fractional Brownian motion: stochastic calculus and applications, Congress of Mathematicians, vol.III, pp.1541-1562, 2006. ,
Long-Range Dependence and Self-Similarity, Cambridge Series in Statistical and Probabilistic Mathematics, 2017. ,
Analysis of approximation methods for differential and integral equations, Applied Mathematical Sciences, vol.57, 1985. ,
Radon-Nikodým derivatives of Gaussian measures, Ann. Math. Statist, vol.37, pp.321-354, 1966. ,
, Generalized Gaussian bridges. Stochastic Process. Appl, vol.124, issue.9, pp.3084-3105, 2014.
Fredholm determinant of a positive definite kernel of a special type and its application, Ann. Math. Statist, vol.43, pp.1914-1926, 1972. ,
Certain asymptotic representations for a Gaussian measure in Hilbert space, Theory of random processes, vol.140, pp.93-104, 1974. ,
Fractional Brownian motion and long-range dependence. Theory and applications of long-range dependence, Birkhäuser Boston, pp.5-38, 2003. ,
Revised and extended from the 2004 French original, Springer Series in Statistics, 2009. ,
Asymptotic distribution of eigenvalues of the kernel in the KirkwoodRiseman integral equation, J. Mathematical Phys, vol.12, pp.83-92, 1971. ,
Properties and numerical evaluation of the Rosenblatt distribution, Bernoulli, vol.19, issue.3, pp.982-1005, 2013. ,
Nonlinear systems analysis, 2ed. SIAM, p.207, 2002. ,
Wenbo Comparison results for the lower tail of Gaussian seminorms, J. Theoret. Probab, vol.5, issue.1, pp.1-31, 1992. ,
When is a linear combination of independent fBm's equivalent to a single fBm? Stochastic Process, Appl, vol.117, issue.1, pp.57-70, 2007. ,