Claims existence, uniqueness, and positivity for a stochastic predator-prey model, but the positivity proof does not rule out hitting zero.
The rosenzweig-macarthur predator-prey model
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Well-Posedness for the Rosenzweig-MacArthur Model with Internal Stochasticity
Claims existence, uniqueness, and positivity for a stochastic predator-prey model, but the positivity proof does not rule out hitting zero.