Modeling with Itô Stochastic Differential Equations

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Stochastic persistence and stationary distribution in a Holling–Tanner type prey–predator model (2012, background): “The available stochastic formalisms can be divided into two broad classes, one of them is known as discrete or continuous time Markov Chain modeling (see [45–50]) and other is the noise added systems [28, 51–65].”
Construction of Equivalent Stochastic Differential Equation Models (2008, methodology): “Also, for the first procedure, similarities are straightforward to obtain between the forward Kolmogorov differential equations satisfied by the probability distributions of the discreteand continuous-time stochastic models and these similarities alow one to infer an Itô SDE model from the discrete ”
Environmental variability and mean-reverting processes (2016, background): “, [3, 4, 5, 6, 8, 10, 18, 21, 23]), it is assumed that changes in the environment produce random changes in a population’s per capita birth and death rates that are independent from the changes due to demographic variability.”