Positivity preserving truncated Euler-Maruyama method for stochastic Lotka-Volterra competition model

The well-known stochastic Lotka{Volterra model for interacting multi-species in
ecology has some typical features: highly nonlinear, positive solution and multi-
dimensional. The known numerical methods including the tamed/truncated Euler-
Maruyama (EM) applied to it do not preserve its positivity. The aim of this paper
is to modify the truncated EM to establish a new positive preserving truncated EM
(PPTEM). To simplify the proof as well as to make our theory more understandable,
we will rst develop a nonnegative preserving truncated EM (NPTEM) and then
establish the PPTEM. Of course, we should point out that the NPTEM has its own
right as many SDE models in applications have their nonnegative solutions.