Positivity preserving logarithmic Euler-Maruyama type scheme for stochastic differential equations (Q2038153)

In this paper, the authors consider the problem of the numerical solution of the following scalar stochastic differential equation \[ dx(t) = b(x(t))dt +\sigma(x(t))dW(t), \] where \(b\) and \(\sigma\) are locally Lipschitz continuous functions. The aim of this paper is to propose a class of explicit positivity preserving numerical methods for the above general class of stochastic differential equations which have positive solutions.