W. Alt, Biased random walk models for chemotaxis and related diffusion approximations, Journal of Mathematical Biology, vol.137, issue.2, pp.147-177, 1980.
DOI : 10.1007/BF00275919

W. Alt, Orientation of cells migrating in a chemotactic gradient, Adv Appl Probab, vol.12, issue.3, pp.566-566, 1980.

L. Lowell, N. G. Baker, and . Hadjiconstantinou, Variance reduction for monte carlo solutions of the boltzmann equation, p.51703, 2005.

A. Bren and M. Eisenbach, How Signals Are Heard during Bacterial Chemotaxis: Protein-Protein Interactions in Sensory Signal Propagation, Journal of Bacteriology, vol.182, issue.24, pp.6865-6873, 2000.
DOI : 10.1128/JB.182.24.6865-6873.2000

F. Chalub, P. Markowich, C. Perthame, and . Schmeiser, Kinetic Models for Chemotaxis and their Drift-Diffusion Limits, Monatshefte f???r Mathematik, vol.142, issue.1-2, pp.123-141, 2004.
DOI : 10.1007/s00605-004-0234-7

G. Dimarco and L. Pareschi, Hybrid Multiscale Methods II. Kinetic Equations, Multiscale Modeling & Simulation, vol.6, issue.4, pp.1169-1197, 2007.
DOI : 10.1137/070680916

E. Weinan and B. Engquist, The heterogeneous multi-scale methods, Comm. Math. Sci, vol.1, issue.1, pp.87-132, 2003.

E. Weinan, B. Engquist, X. Li, W. Ren, and E. Vanden-eijnden, Heterogeneous multiscale methods: A review, Commun Comput Phys, vol.2, issue.3, pp.367-450, 2007.

R. Erban and H. Othmer, From Individual to Collective Behavior in Bacterial Chemotaxis, SIAM Journal on Applied Mathematics, vol.65, issue.2, pp.361-391, 2004.
DOI : 10.1137/S0036139903433232

R. Erban and H. Othmer, : A Paradigm for Multiscale Modeling in Biology, Multiscale Modeling & Simulation, vol.3, issue.2, pp.362-394, 2005.
DOI : 10.1137/040603565

C. W. Gear, C. Kevrekidis, and . Theodoropoulos, ???Coarse??? integration/bifurcation analysis via microscopic simulators: micro-Galerkin methods, Computers & Chemical Engineering, vol.26, issue.7-8, pp.941-963, 2002.
DOI : 10.1016/S0098-1354(02)00020-0
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.23.3768

T. Hillen and H. Othmer, The diffusion limit of transport equations derived from velocity-jump processes, SIAM Journal on Applied Mathematics, vol.61, issue.3, pp.751-775, 2000.

D. Horstman, From 1970 until present: the Keller?Segel model in chemotaxis and its consequences I, Jahresber. Deutsh. Math.-Verein, vol.105, issue.3, pp.103-165, 2003.

D. Horstman, From 1970 until present: the Keller?Segel model in chemotaxis and its consequences II, Jahresber. Deutsh. Math.-Verein, vol.106, issue.2, pp.51-69, 2004.

E. Keller and L. Segel, Initiation of slime mold aggregation viewed as an instability, Journal of Theoretical Biology, vol.26, issue.3, pp.399-415, 1970.
DOI : 10.1016/0022-5193(70)90092-5

I. Kevrekidis, C. Gear, . Hyman, . Kevrekidis, C. Runborg et al., Equation-free, coarse-grained multiscale computation: enabling microscopic simulators to perform system-level tasks, Comm. Math. Sciences, vol.1, issue.4, pp.715-762, 2003.

G. Ioannis, G. Kevrekidis, and . Samaey, Equation-free multiscale computation: Algorithms and applications, Annu Rev Phys Chem, vol.60, pp.321-344, 2009.

P. Kloeden and E. Platen, Numerical solution of stochastic differential equations, Applications of Mathematics, vol.23, 1992.

J. R. Norris, Markov chains, volume 2 of Cambridge Series in Statistical and Probabilistic Mathematics, 1998.

H. Othmer, W. Dunbar, and . Alt, Models of dispersal in biological systems, Journal of Mathematical Biology, vol.25, issue.3, pp.263-298, 1988.
DOI : 10.1007/BF00277392

H. Othmer and T. Hillen, The Diffusion Limit of Transport Equations II: Chemotaxis Equations, SIAM Journal on Applied Mathematics, vol.62, issue.4, pp.1222-1250, 2002.
DOI : 10.1137/S0036139900382772

C. Patlak, Random walk with persistence and external bias, The Bulletin of Mathematical Biophysics, vol.198, issue.3, pp.311-338, 1953.
DOI : 10.1007/BF02476407

M. Rousset and G. Samaey, Individual-based models for bacterial chemotaxis in the diffusion limit, Mathematical Models and Methods in Applied Sciences, 2010.

D. W. Scott, Multivariate density estimation: theory, practice, and visualization, 1992.
DOI : 10.1002/9781118575574

B. W. Silverman, Density estimation for statistics and data analysis, of Monographs on Statistics and Applied Probability. Chapman and Hall, 1986.
DOI : 10.1007/978-1-4899-3324-9

A. Stock, A nonlinear stimulus-response relation in bacterial chemotaxis, Proceedings of the National Academy of Sciences, vol.96, issue.20, pp.10945-10947, 1999.
DOI : 10.1073/pnas.96.20.10945

A. Appendix, Technical lemmas, used in proof of Theorem 4

L. Appendix and A. , Let (? n ) n?1 a sequence of independent exponential random variables with mean 1, and (T n ) n?1 a strictly increasing sequence of random times with T 0 = 0 such that: ? For any m ? 1, the sequence (? n ) n?m+1 is independent of the past