Abstract
A stochastic version of the classical Lotka–Volterra predator–prey model is considered. Using hidden Markov models techniques, we derive a Zakai equation driven by Poisson martingales related to the distribution of the number of individuals in a two-species (predator–prey) animal population. Partial information is provided by a continuous-time version of the so-called capture–recapture sampling technique. By using a gauge transformation a stochastic differential equation is transformed into a linear ordinary differential equations.
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