H. Alexandersson, A Simple Stochastic Model of the Precipitation Process, Journal of Climate and Applied Meteorology, vol.24, issue.12, pp.1285-1295, 1985.
DOI : 10.1175/1520-0450(1985)024<1285:ASSMOT>2.0.CO;2

G. A. Athanassoulis and P. N. Gavriliadis, The truncated Hausdorff moment problem solved by using kernel density functions, Probabilistic Engineering Mechanics, vol.17, issue.3, pp.273-291, 2002.
DOI : 10.1016/S0266-8920(02)00012-7

L. D. Brown, A. V. Carter, M. G. Low, and C. Zhang, Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift. The Annals of Statistics, pp.2074-2097, 2004.

R. Cont, D. Larrard, and A. , Price Dynamics in a Markovian Limit Order Market, SIAM Journal on Financial Mathematics, vol.4, issue.1, pp.1-25, 2013.
DOI : 10.1137/110856605

URL : https://hal.archives-ouvertes.fr/hal-00832155

C. Duval and M. Hoffmann, Statistical inference across time scales, Electronic Journal of Statistics, vol.5, issue.0, pp.2004-2030, 2011.
DOI : 10.1214/11-EJS660

URL : https://hal.archives-ouvertes.fr/hal-00692996

H. U. Gerber and E. Shiu, Pricing Perpetual Options for Jump Processes, North American Actuarial Journal, vol.6, issue.2, pp.101-112, 1998.
DOI : 10.1080/10920277.1998.10595671

F. Guilbaud and H. Pham, Optimal high-frequency trading in a pro-rata microstructure with predictive information, Arxiv preprint 1205, pp.3051-3052, 2012.

K. J. Hong and S. Satchell, Defining Single Asset Price Momentum in terms of a Stochastic Process, Theoretical Economics Letters, vol.02, issue.03, pp.274-277, 2012.
DOI : 10.4236/tel.2012.23050

M. Kotulski, Asymptotic distributions of continuous-time random walks: A probabilistic approach, Journal of Statistical Physics, vol.83, issue.64, pp.777-792, 1995.
DOI : 10.1007/BF02179257

L. Cam, L. Yang, and L. G. , Asymptotics in Statistics: Some Basic Concepts, 2000.

J. B. Levy and M. S. Taqqu, Renewal Reward Processes with Heavy-Tailed Inter-Renewal Times and Heavy-Tailed Rewards, Bernoulli, vol.6, issue.1, pp.23-44, 2000.
DOI : 10.2307/3318631

J. Masoliver, M. Montero, J. Perelló, and G. H. Weiss, Direct and inverse problems with some generalizations and extensions. Arxiv preprint, pp.308017-308019, 2008.
DOI : 10.1016/j.physa.2007.01.001

URL : http://arxiv.org/abs/cond-mat/0308017

R. Metzler and J. Klafter, The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics, Journal of Physics A: Mathematical and General, vol.37, issue.31, pp.161-208, 2004.
DOI : 10.1088/0305-4470/37/31/R01

T. Mikosch, ¨. Onalan, and ¨. O. , Non-life Insurance Mathematics: An Introduction with the Poisson Process Fractional Ornstein-Uhlenbeck Processes Driven by Stable Lévy Motion in Finance, International Research Journal of Finance and Economics, vol.16, issue.42, pp.129-139, 2009.
DOI : 10.1007/978-3-540-88233-6

G. Rodriguez and S. Seatzu, On the solution of the finite moment problem, Journal of Mathematical Analysis and Applications, vol.171, issue.2, pp.321-333, 1992.
DOI : 10.1016/0022-247X(92)90346-F

J. R. Russell and R. F. Engle, A Discrete-State Continuous-Time Model of Financial Transactions Prices and Times, Journal of Business & Economic Statistics, vol.23, issue.2, 2005.
DOI : 10.1198/073500104000000541

I. Shevtsova, On the accuracy of the normal approximation to the distributions of Poisson random sums, PAMM, vol.35, issue.1, pp.2080025-2080026, 2007.
DOI : 10.1002/pamm.200701074

K. Sobezyk and J. Tre¸bickitre¸bicki, Maximum entropy principle in stochastic dynamics, Probabilistic Engineering Mechanics, vol.5, issue.3, pp.102-110, 1990.
DOI : 10.1016/0266-8920(90)90001-Z

A. Tagliani, Hausdorff moment problem and maximum entropy: A unified approach, Applied Mathematics and Computation, vol.105, issue.2-3, pp.291-305, 1999.
DOI : 10.1016/S0096-3003(98)10084-X

A. Tsybakov, Introduction to Nonparametric Estimation, 2008.
DOI : 10.1007/b13794

V. V. Uchaikin and V. M. Zolotarev, Chance and stability. Stable Distributions and their Applications, VSP, 1999.

G. Watson, A Treatise on the Theory of Bessel Functions, The Mathematical Gazette, vol.18, issue.231, 1922.
DOI : 10.2307/3605513