Abstract
Abstract The fixed time step integration method proposed in Grigoriu (2009) [2] is used to construct recurrence formulas for generating samples of processes X ( t ) satisfying stochastic differential equations (SDEs) with Gaussian (GWN) and Poisson white noise (PWN). Theoretical arguments and numerical examples are employed to show that the sequence of processes X n ( t ) defined by these recurrence formulas can be used to assess the stability of the trivial solution of SDEs with linear drift and diffusion coefficients driven by GWN and/or PWN and capture the phase transition phenomenon exhibited by the state of a randomized Verhulst model for population growth.
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