A. Andersen, R. Cont, and E. Vinkovskaya, A point process model for the high-frequency dynamics of a limit order book, Financial Engineering Report, pp.2010-2018, 2010.

V. Araman and P. Glynn, Fractional brownian motion with H < 1/2 as a limit of scheduled traffic, 2011.

M. Avellaneda, S. Stoikov, and J. Reed, Forecasting prices from Level-I quotes in the presence of hidden liquidity, Algorithmic Finance, vol.1, pp.35-43, 2011.

F. Baccelli and G. Fayolle, Analysis of Models Reducible to a Class of Diffusion Processes in the Positive Quarter Plane, SIAM Journal on Applied Mathematics, vol.47, issue.6, pp.1367-1385, 1987.
DOI : 10.1137/0147090

E. Bacry, S. Delattre, M. Hoffman, and J. Muzy, Scaling limits for Hawkes processes and application to financial statistics, 2010.

E. Bayraktar, U. Horst, and R. Sircar, A Limit Theorem for Financial Markets with Inert Investors, Mathematics of Operations Research, vol.31, issue.4, pp.33-54, 2006.
DOI : 10.1287/moor.1060.0202

B. Biais, P. Hillion, and C. Spatt, An Empirical Analysis of the Limit Order Book and the Order Flow in the Paris Bourse, The Journal of Finance, vol.14, issue.5, pp.1655-1689, 1995.
DOI : 10.1111/j.1540-6261.1995.tb05192.x

J. P. Bouchaud, M. Mezard, and M. Potters, Statistical properties of stock order books: empirical results and models, Quantitative Finance, vol.2, issue.4, p.251, 2002.
DOI : 10.1103/PhysRevE.62.R4493

URL : https://hal.archives-ouvertes.fr/hal-00002329

J. Bouchaud, D. Farmer, and F. Lillo, How markets slowly digest changes in supply and demand Handbook of Financial Markets: Dynamics and Evolution, pp.57-160, 2008.

P. Bougerol and N. Picard, Strict Stationarity of Generalized Autoregressive Processes, The Annals of Probability, vol.20, issue.4, pp.1714-1730, 1992.
DOI : 10.1214/aop/1176989526

R. Cont, Statistical Modeling of High-Frequency Financial Data, IEEE Signal Processing Magazine, vol.28, issue.5, pp.16-25, 2011.
DOI : 10.1109/MSP.2011.941548

URL : https://hal.archives-ouvertes.fr/hal-00704766

R. Cont and A. De-larrard, Price dynamics in a markovian limit order market. Working paper. URL http, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00552252

R. Cont, A. Kukanov, and S. Stoikov, The price impact of order book events. Working paper, SSRN. URL http, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00545745

R. Cont, S. Stoikov, and R. Talreja, A Stochastic Model for Order Book Dynamics, Operations Research, vol.58, issue.3, pp.549-563, 2010.
DOI : 10.1287/opre.1090.0780

URL : https://hal.archives-ouvertes.fr/hal-00497666

J. G. Dai and V. Nguyen, On the Convergence of Multiclass Queueing Networks in Heavy Traffic, The Annals of Applied Probability, vol.4, issue.1, pp.26-42, 1994.
DOI : 10.1214/aoap/1177005199

R. Engle and J. Russell, Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data, Econometrica, vol.66, issue.5, pp.1127-1162, 1998.
DOI : 10.2307/2999632

R. F. Engle, The Econometrics of Ultra-high-frequency Data, Econometrica, vol.68, issue.1, pp.1-22, 2000.
DOI : 10.1111/1468-0262.00091

E. I. Galakhov and A. L. Skubachevskii, On Feller Semigroups Generated by Elliptic Operators with Integro-differential Boundary Conditions, Journal of Differential Equations, vol.176, issue.2, pp.315-355, 2001.
DOI : 10.1006/jdeq.2000.3976

E. Ghysels and J. Jasiak, GARCH for Irregularly Spaced Financial Data: The ACD-GARCH Model, Studies in Nonlinear Dynamics & Econometrics, vol.2, issue.4, pp.133-149, 1998.
DOI : 10.2202/1558-3708.1035

P. Gopikrishnan, V. Plerou, X. Gabaix, and H. E. Stanley, Statistical properties of share volume traded in financial markets, Physical Review E, vol.62, issue.4, pp.4493-4496, 2000.
DOI : 10.1103/PhysRevE.62.R4493

J. Harrison and . Michael, The diffusion approximation for tandem queues in heavy traffic, Advances in Applied Probability, vol.11, issue.04, pp.886-905, 1978.
DOI : 10.1002/cpa.3160240206

J. Harrison, V. Michael, and . Nguyen, Brownian models of multiclass queueing networks: Current status and open problems, Queueing Systems, vol.75, issue.1-3, pp.5-40, 1993.
DOI : 10.1007/BF01158927

J. Hasbrouck, Empirical Market Microstructure, 2007.

N. Hautsch, Modelling Irregularly Spaced Financial Data, 2004.
DOI : 10.1007/978-3-642-17015-7

D. L. Iglehart and W. Whitt, Multiple channel queues in heavy traffic. I. Advances in Appl, Probability, vol.2, pp.150-177, 1970.

D. L. Iglehart and W. Whitt, The Equivalence of Functional Central Limit Theorems for Counting Processes and Associated Partial Sums, The Annals of Mathematical Statistics, vol.42, issue.4, pp.1372-1378, 1971.
DOI : 10.1214/aoms/1177693249

S. Iyengar, Hitting Lines with Two-Dimensional Brownian Motion, SIAM Journal on Applied Mathematics, vol.45, issue.6, pp.983-989, 1985.
DOI : 10.1137/0145060

J. Jacod and A. N. Shiryaev, Limit theorems for stochastic processes, 2003.
DOI : 10.1007/978-3-662-02514-7

L. Kruk, Functional Limit Theorems for a Simple Auction, Mathematics of Operations Research, vol.28, issue.4, pp.716-751, 2003.
DOI : 10.1287/moor.28.4.716.20519

T. Lindvall, Weak convergence of probability measures and random functions in the function space D[0,???), Journal of Applied Probability, vol.1, issue.01, pp.109-121, 1973.
DOI : 10.1090/S0002-9939-1963-0153046-2

A. Lipton, Mathematical methods in foreign exchange, 2001.
DOI : 10.1142/4694

S. Maslov and M. Mills, Price fluctuations from the order book perspective???empirical facts and a simple model, Physica A: Statistical Mechanics and its Applications, vol.299, issue.1-2, p.234, 2001.
DOI : 10.1016/S0378-4371(01)00301-6

H. Mendelson, Market Behavior in a Clearing House, Econometrica, vol.50, issue.6, pp.1505-1524, 1982.
DOI : 10.2307/1913393

A. Metzler, On the first passage problem for correlated Brownian motion, Statistics & Probability Letters, vol.80, issue.5-6, pp.5-6, 2010.
DOI : 10.1016/j.spl.2009.11.001

K. Ramanan and M. I. Reiman, Fluid and heavy traffic diffusion limits for a generalized processor sharing model, The Annals of Applied Probability, vol.13, issue.1, pp.100-139, 2003.
DOI : 10.1214/aoap/1042765664

S. Resnick, Heavy-tail phenomena: Probabilistic and Statistical Modeling, 2006.

E. Smith, J. D. Farmer, L. Gillemot, and S. Krishnamurthy, Statistical theory of the continuous double auction, Quantitative Finance, vol.3, issue.6, pp.481-514, 2003.
DOI : 10.1017/CBO9780511755767

F. Spitzer, Some theorems concerning 2-dimensional brownian motion, Transactions of the American Mathematical Society, vol.87, pp.187-197, 1958.

K. Taira, On the existence of Feller semigroups with boundary conditions, Memoirs of the American Mathematical Society, vol.99, issue.475, 1991.
DOI : 10.1090/memo/0475

W. Whitt, Some Useful Functions for Functional Limit Theorems, Mathematics of Operations Research, vol.5, issue.1, pp.67-85, 1980.
DOI : 10.1287/moor.5.1.67

W. Whitt, Stochastic Process Limits, 2002.

H. Yoshida and I. Miyamoto, Harmonic Functions in a Cone Which Vanish on the Boundary, Mathematische Nachrichten, vol.50, issue.1, pp.177-187, 1999.
DOI : 10.1002/mana.19992020115

C. Zhou, An Analysis of Default Correlations and Multiple Defaults, Review of Financial Studies, vol.14, issue.2, pp.555-576, 2001.
DOI : 10.1093/rfs/14.2.555