F. Antonelli, Backward-forward stochastic differential equations, Ann. Appl. Probab, vol.3, pp.777-793, 1993.

V. I. Arnold, Sur la topologie des écoulements stationnaires des fluides parfaits, C. R. Acad. Sc, vol.261, pp.17-20, 1965.

E. Beltrami, Translated by Dr. Giuseppe Filipponi from original paper appeared in 1889 in Rendiconti del Reale Instítuto Lombardo, Int. J. Fusion Energy, vol.3, pp.53-57, 1985.

S. Benachour, B. Roynette, and P. Vallois, Branching process associated with 2 -Navier Stokes equation, Rev. Mat. Iberoam, vol.17, pp.331-373, 2001.

R. N. Bhattacharya, L. Chen, S. Dobson, R. B. Guenther, C. Orum et al., Majorizing kernels and stochastic cascades with applications to incompressible Navier-Stokes equations, Trans. Amer. Math. Soc, vol.355, pp.5003-5040, 2003.

B. Bouchard and S. Menozzi, Strong approximations of BSDEs in a domain, Bernoulli, vol.15, pp.1117-1147, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00446316

M. E. Brachet, U. Frisch, D. I. Meiron, R. H. Morf, B. G. Nickel et al., Small-scale structure of the Taylor-Green vortex, J. Fluid Mech, vol.130, pp.411-452, 1983.

J. M. Burgers, A mathematical model illustrating the theory of turbulence, Adv. Appl. Mech, vol.1, pp.171-199, 1948.

J. Chemin, B. Desjardins, I. Gallagher, and E. Grenier, Mathematical Geophysics -An introduction to rotating fluids and the Navier-Stokes equations, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00112069

P. Cheridito, H. M. Soner, N. Touzi, and N. Victoir, Second-order backward stochastic differential equations and fully nonlinear parabolic PDEs, Comm. Pure Appl. Math, vol.60, pp.1081-1110, 2007.

S. Childress, New solutions of the kynematic dynamo problem, J. Math. Phys, vol.11, pp.3063-3076, 1970.

A. J. Chorin, A numerical method for solving incompressible viscous flow problems, J. Comput. Phys, vol.2, pp.12-26, 1967.

A. J. Chorin, Numerical solution of the Navier-Stokes equations, Math. Comp, vol.22, pp.745-762, 1968.

A. J. Chorin, On the convergence of discrete approximations to the Navier-Stokes equations, Math. Comp, vol.23, pp.341-353, 1969.

A. J. Chorin, Numerical study of slightly viscous flow, J. Fluid Mech, vol.57, pp.785-796, 1973.

A. J. Chorin, Vorticity and turbulence, 1998.

P. Constantin and G. Iyer, A stochastic Lagrangian representation of the three-dimensional incompressible Navier-Stokes equations, Comm. Pure Appl. Math, vol.61, pp.330-345, 2008.

P. Constantin and G. Iyer, A stochastic-Lagrangian approach to the Navier-Stokes equations in domains with boundary, Ann. Appl. Probab, vol.21, pp.1466-1492, 2011.

S. Corlay and G. Pagès, Functional quantization-based stratified sampling methods, Monte Carlo Methods Appl, vol.21, pp.1-32, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00464088

S. Corlay, G. Pagès, and J. Printems, The optimal quantization website, 2005.

M. G. Crandall, H. Ishii, and P. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc, vol.27, pp.1-67, 1992.

A. B. Cruzeiro and E. Shamarova, Navier-Stokes equations and forward-backward SDEs on the group of diffeomorphisms of a torus, Stoch. Proc. Appl, vol.119, pp.4034-4060, 2009.

F. Delarue, On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case, Stoch. Proc. Appl, vol.99, pp.209-286, 2002.

F. Delarue and S. Menozzi, A forward-backward stochastic algorithm for quasi-linear PDEs, Ann. Appl. Probab, vol.16, pp.140-184, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00002980

F. Delarue and S. Menozzi, An interpolated stochastic algorithm for quasi-linear PDEs, Math. Comp, vol.77, pp.125-158, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00021967

F. Delbaen, J. Qiu, and S. Tang, Forward-backward stochastic differential systems associated to Navier-Stokes equations in the whole space, Stoch. Proc. Appl, vol.125, pp.2516-2561, 2015.

. Euler, Principes généraux du mouvement des fluides, Mém. Acad. Roy. Sci. Berlin, vol.11, pp.274-315, 1757.

C. L. Fefferman, Existence and smoothness of the Navier-Stokes equation, 2000.

R. P. Feynman, Space-time approach to non-relativistic quantum mechanics, Rev. Mod. Phys, vol.20, pp.367-387, 1948.

G. S. Fishman, A first course in Monte Carlo, 2005.

C. Foias, O. Manley, R. Rosa, and R. Teman, Navier-Stokes equations and turbulence, of Encyclopedia of Mathematics and its Applications, vol.83, 2001.

J. Fontbona, Stochastic vortex method for forced three-dimensional Navier-Stokes equations and pathwise convergence rate, Ann. Appl. Probab, vol.20, pp.1761-1800, 2010.

J. Fontbona and S. Méléard, A random space-time birth particle method for 2 vortex equations with external fields, Math. Comp, vol.77, issue.263, pp.1525-1558, 2008.

S. Graf and H. Luschgy, Foundations of quantization for probability distributions, Lecture Notes in Mathematics, vol.1730, 2000.

K. Itô, Stochastic integral, Proc. Imp. Acad. Tokyo, vol.20, pp.519-524, 1944.

K. Itô, On a stochastic integral equation, Proc. Japan Acad, vol.22, pp.32-35, 1946.

G. Iyer and J. Mattingly, A stochastic-Lagrangian particle system for the Navier-stokes equations, Nonlinearity, vol.21, pp.2537-2553, 2008.

M. Kac, On distributions of certain Wiener functionals, Trans. Amer. Math. Soc, vol.65, issue.1, pp.1-13, 1949.

A. W. Kolkiewicz, Efficient Monte Carlo simulation for integral functionals of Brownian motion, J. Complexity, vol.30, pp.255-278, 2014.

Y. , L. Jan, and A. S. Sznitman, Stochastic cascades and 3-dimensional Navier-Stokes equations, vol.109, pp.343-366, 1997.

A. Lejay and V. Reutenauer, A variance reduction technique using a quantized Brownian motion as a control variate, J. Comput. Finance, vol.16, pp.61-84, 2012.
URL : https://hal.archives-ouvertes.fr/inria-00393749

J. Ma and J. Yong, Forward-backward stochastic differential equations and their applications, Lecture Notes in Mathematics, vol.1702, 1999.

J. Ma, P. Protter, and J. Yong, Solving forward-backward stochastic differential equations explicitly -a four step scheme, Probab. Theory Relat. Fields, vol.98, issue.3, pp.339-359, 1994.

A. J. Majda and A. L. Bertozzi, Vorticity and incompressible flow, 2002.

X. Mao, Backward stochastic differential equations and quasilinear partial differential equations, Stochastic Partial Differential Equations, vol.216, pp.189-208, 1995.

H. A. Mardones-gonzález, Numerical solution of stochastic differential equations with multiplicative noise, 2017.

S. Méléard, Stochastic particle approximations for two-dimensional Navier-Stokes equations, Dynamics and Randomness II, vol.10, pp.147-197, 2004.

R. Mikulevicius and E. Platen, Rate of convergence of the Euler approximation for diffusion processes, Math. Nachr, vol.151, pp.233-239, 1991.

G. N. Milstein and M. V. Tretyakov, Discretization of forward-backward stochastic differential equations and related quasi-linear parabolic equations, IMA J. Numer. Anal, vol.27, issue.1, pp.24-44, 2007.

G. N. Milstein and M. V. Tretyakov, Solving the Dirichlet problem for Navier-Stokes equations by probabilistic approach, BIT Numer. Math, vol.52, pp.141-153, 2012.

G. N. Milstein and M. V. Tretyakov, Probabilistic methods for the incompressible Navier-Stokes equations with space periodic conditions, Adv. Appl. Prob, vol.45, pp.742-772, 2013.

C. Navier, Mémoire sur les lois du mouvement des fluides, Mem. Acad. Sci. Inst. France, vol.6, pp.389-440, 1822.

M. Ossiander, A probabilistic representation of solutions of the incompressible Navier-Stokes equations in R 3, Probab. Theory Relat. Fields, vol.133, pp.267-298, 2005.

G. Pagès and J. Printems, Optimal quadratic quantization for numerics: the Gaussian case, Monte Carlo Methods Appl, vol.9, pp.135-165, 2003.

G. Pagès and J. Printems, Functional quantization for numerics with an application to option pricing, Monte Carlo Methods Appl, vol.11, pp.407-446, 2005.

É. Pardoux, Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic PDEs of second order, Stochastic Analysis and Related Topics VI, pp.79-127, 1998.

É. Pardoux and S. Peng, Backward stochastic differential equations and quasilinear parabolic partial differential equations, Stochastic Partial Differential Equations and Their Applications, vol.176, pp.200-217, 1992.

É. Pardoux and S. G. Peng, Adapted solution of a backward stochastic differential equation, Syst. Control Lett, vol.14, pp.55-61, 1990.

É. Pardoux and S. Tang, Forward-backward stochastic differential equations and quasilinear parabolic PDEs, vol.114, pp.123-150, 1999.

G. A. Pavliotis, A. M. Stuart, and K. C. Zygalakis, Calculating effective diffusivities in the limit of vanishing molecular diffusion, J. Comput. Phys, vol.228, pp.1030-1055, 2009.

A. Shapiro, The use of an exact solution of the Navier-Stokes equations in a validation test of a three-dimensional nonhydrostatic numerical model, Mon. Weather Rev, vol.121, pp.2420-2425, 1993.

G. G. Stokes, On the theories of the internal friction of fluids in motion, and of the equilibrium and motion of elastic solids, Trans. Camb. Phil. Soc, vol.8, pp.287-319, 1849.

D. Talay and O. Vaillant, A stochastic particle method with random weights for the computation of statistical solutions of McKean-Vlasov equations, Ann. Appl. Probab, vol.13, issue.1, pp.140-180, 2003.
URL : https://hal.archives-ouvertes.fr/inria-00072261

L. Tartar, An introduction to Navier-Stokes equation and Oceanography, 2006.

M. Tavelli and M. Dumbser, A staggered space-time discontinuous Galerkin method for the three-dimensional incompressible Navier-Stokes equations on unstructured tetrahedral meshes, J. Comput. Phys, vol.319, pp.294-323, 2016.

G. I. Taylor and A. E. Green, Mechanism of the production of small eddies from large ones, Proc. R. Soc. Lond. A, vol.158, pp.499-521, 1937.

E. C. Waymire, Probability & incompressible Navier-Stokes equations: An overview of some recent developments, Probab. Surv, vol.2, pp.1-32, 2005.

X. Zhang, A stochastic representation for backward incompressible Navier-Stokes equations, vol.148, pp.305-332, 2010.