Cuadro de texto: Looking for relationships with continuous models
A more rigurous approach: Fock space (or Doi-Peliti) techniques 
(equivalent to a Poisson representation) Cuadro de texto: Put the bugs in a lattice (of L sites), and consider the number of bugs at each site (N1,N2,…,NL).
Write the Master Equation for the time evolution of the probabilities of these numbers.
Represent the Master Equation in terms of a (quantum mechanical like) Hamiltonian constructed with creation and annihilation operators.  
Find the action associated to that Hamiltonian. Go again off-lattice by performing the continuum limit. 
Approximate the action by keeping only quadratic terms, so that a Langevin equation for an auxiliary density-like field can be extracted from it.

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