P. C. Hohenberg and B. I. Halperin, Theory of dynamic critical phenomena, Reviews of Modern Physics, vol.49, issue.3, p.435, 1977.
DOI : 10.1103/RevModPhys.49.435

C. W. Gardiner and S. Chaturvedi, The poisson representation. I. A new technique for chemical master equations, Journal of Statistical Physics, vol.270, issue.6, p.429, 1977.
DOI : 10.1007/BF01014349

D. S. Dean, Langevin equation for the density of a system of interacting Langevin processes, Journal of Physics A: Mathematical and General, vol.29, issue.24, p.613, 1996.
DOI : 10.1088/0305-4470/29/24/001

A. Andreanov, G. Biroli, J. Bouchaud, and A. Lefèvre, Field theories and exact stochastic equations for interacting particle systems, Physical Review E, vol.74, issue.3, p.30101, 2006.
DOI : 10.1103/PhysRevE.74.030101

URL : http://arxiv.org/abs/cond-mat/0602307

K. Itakura, J. Ohkubo, and S. Sasa, Two Langevin equations in the Doi???Peliti formalism, Journal of Physics A: Mathematical and Theoretical, vol.43, issue.12, p.125001, 2010.
DOI : 10.1088/1751-8113/43/12/125001

J. Marro and R. Dickman, Nonequilibrium phase transitions in lattice models, 2005.
DOI : 10.1017/CBO9780511524288

U. C. Täuber, M. Howard, and B. P. Vollmayr-lee, Applications of field-theoretic renormalization group methods to reaction???diffusion problems, Journal of Physics A: Mathematical and General, vol.38, issue.17, p.79, 2005.
DOI : 10.1088/0305-4470/38/17/R01

M. Doi, Second quantization representation for classical many-particle system, Journal of Physics A: Mathematical and General, vol.9, issue.9, p.1465, 1976.
DOI : 10.1088/0305-4470/9/9/008

M. Doi, Stochastic theory of diffusion-controlled reaction, Journal of Physics A: Mathematical and General, vol.9, issue.9, p.1479, 1976.
DOI : 10.1088/0305-4470/9/9/009

L. Peliti, Path integral approach to birth-death processes on a lattice, Journal de Physique, vol.46, issue.9, p.1469, 1985.
DOI : 10.1051/jphys:019850046090146900

URL : https://hal.archives-ouvertes.fr/jpa-00210092

M. J. Howard and U. C. Täuber, `Real' versus `imaginary' noise in diffusion-limited reactions, Journal of Physics A: Mathematical and General, vol.30, issue.22, p.7721, 1997.
DOI : 10.1088/0305-4470/30/22/011

M. A. Muñoz, Nature of different types of absorbing states, Physical Review E, vol.57, issue.2, p.1377, 1998.
DOI : 10.1103/PhysRevE.57.1377

O. Deloubrì-ere, L. Frachebourg, H. Hilhorst, and K. Kitahara, Imaginary noise and parity conservation in the reaction A+A???0, Physica A: Statistical Mechanics and its Applications, vol.308, issue.1-4, p.135, 2002.
DOI : 10.1016/S0378-4371(02)00548-4

D. Gredat, I. Dornic, and J. Luck, On an imaginary exponential functional of Brownian motion, Journal of Physics A: Mathematical and Theoretical, vol.44, issue.17, p.175003, 2011.
DOI : 10.1088/1751-8113/44/17/175003

K. J. Wiese, Coherent-state path integral versus coarse-grained effective stochastic equation of motion: From reaction diffusion to stochastic sandpiles, Physical Review E, vol.93, issue.4, p.42117, 2016.
DOI : 10.1103/PhysRevE.93.042117

T. Liggett, Interacting particle systems, 2005.

G. Schütz and S. Sandow, Non-Abelian symmetries of stochastic processes: Derivation of correlation functions for random-vertex models and disordered-interacting-particle systems, Physical Review E, vol.49, issue.4, p.2726, 1994.
DOI : 10.1103/PhysRevE.49.2726

C. R. Doering, C. Mueller, and P. Smereka, Interacting particles, the stochastic Fisher???Kolmogorov???Petrovsky???Piscounov equation, and duality, Physica A: Statistical Mechanics and its Applications, vol.325, issue.1-2, p.243, 2003.
DOI : 10.1016/S0378-4371(03)00203-6

C. Giardina, J. Kurchan, F. Redig, and K. Vafayi, Duality and Hidden Symmetries in Interacting Particle Systems, Journal of Statistical Physics, vol.9, issue.3, p.25, 2009.
DOI : 10.1007/s10955-009-9716-2

J. Ohkubo, Duality in Interacting Particle Systems and Boson Representation, Journal of Statistical Physics, vol.37, issue.3, p.454, 2010.
DOI : 10.1007/s10955-009-9910-2

URL : http://arxiv.org/abs/0909.5290

C. W. Gardiner, Handbook of stochastic methods, 1985.

V. Elgart and A. Kamenev, Rare event statistics in reaction-diffusion systems, Physical Review E, vol.70, issue.4, p.41106, 2004.
DOI : 10.1103/PhysRevE.70.041106

I. Dornic, H. Chaté, and M. A. Muñoz, Integration of Langevin Equations with Multiplicative Noise and the Viability of Field Theories for Absorbing Phase Transitions, Physical Review Letters, vol.94, issue.10, p.100601, 2005.
DOI : 10.1103/PhysRevLett.94.100601

O. Hammal, H. Chaté, I. Dornic, and M. A. Muñoz, Langevin Description of Critical Phenomena with Two Symmetric Absorbing States, Physical Review Letters, vol.94, issue.23, p.230601, 2005.
DOI : 10.1103/PhysRevLett.94.230601

D. I. Russell and R. A. Blythe, Noise-Induced Dynamical Transition in Systems with Symmetric Absorbing States, Physical Review Letters, vol.106, issue.16, p.165702, 2011.
DOI : 10.1103/PhysRevLett.106.165702

T. Biancalani, L. Dyson, and A. J. Mckane, Noise-Induced Bistable States and Their Mean Switching Time in Foraging Colonies, Physical Review Letters, vol.112, issue.3, p.38101, 2014.
DOI : 10.1103/PhysRevLett.112.038101

URL : http://doi.org/10.1103/physrevlett.112.038101

S. Pigolotti and R. Benzi, Selective Advantage of Diffusing Faster, Physical Review Letters, vol.112, issue.18, p.188102, 2014.
DOI : 10.1103/PhysRevLett.112.188102

F. Jafarpour, T. Biancalani, and N. Goldenfeld, Noise-Induced Mechanism for Biological Homochirality of Early Life Self-Replicators, Physical Review Letters, vol.115, issue.15, p.158101, 2015.
DOI : 10.1103/PhysRevLett.115.158101

E. Moro, Hybrid method for simulating front propagation in reaction-diffusion systems, Physical Review E, vol.69, issue.6, p.60101, 2004.
DOI : 10.1103/PhysRevE.69.060101

E. Moro, Numerical schemes for continuum models of reaction-diffusion systems subject to internal noise, Physical Review E, vol.70, issue.4, p.45102, 2004.
DOI : 10.1103/PhysRevE.70.045102

E. Moro and H. Schurz, Boundary Preserving Semianalytic Numerical Algorithms for Stochastic Differential Equations, SIAM Journal on Scientific Computing, vol.29, issue.4, p.1525, 2007.
DOI : 10.1137/05063725X

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.259.9437

U. C. Täuber, Critical dynamics: a field theory approach to equilibrium and non-equilibrium scaling behavior, 2014.
DOI : 10.1017/CBO9781139046213

P. C. Martin, E. Siggia, and H. Rose, Statistical Dynamics of Classical Systems, Physical Review A, vol.8, issue.1, p.423, 1973.
DOI : 10.1103/PhysRevA.8.423

L. Canet, H. Chaté, B. Delamotte, I. Dornic, and M. A. Muñoz, Nonperturbative Fixed Point in a Nonequilibrium Phase Transition, Physical Review Letters, vol.95, issue.10, p.100601, 2005.
DOI : 10.1103/PhysRevLett.95.100601

URL : https://hal.archives-ouvertes.fr/hal-00380735

O. Hallatschek and K. S. Korolev, Fisher Waves in the Strong Noise Limit, Physical Review Letters, vol.103, issue.10, p.108103, 2009.
DOI : 10.1103/PhysRevLett.103.108103

K. S. Korolev, M. Avlund, O. Hallatschek, and D. R. Nelson, Genetic demixing and evolution in linear stepping stone models, Reviews of Modern Physics, vol.82, issue.2, p.1691, 2010.
DOI : 10.1103/RevModPhys.82.1691

M. A. Muñoz, G. Grinstein, and Y. Tu, Survival probability and field theory in systems with absorbing states, Physical Review E, vol.56, issue.5, p.5101, 1997.
DOI : 10.1103/PhysRevE.56.5101

H. Janssen, Survival and percolation probabilities in the field theory of growth models, Journal of Physics: Condensed Matter, vol.17, issue.20, p.1973, 2005.
DOI : 10.1088/0953-8984/17/20/021