A note on pathwise stability and positivity of nonlinear stochastic differential equations
Numerical Analysis
2017-08-29 v1
Abstract
We use the semi-discrete method, originally proposed in Halidias (2012), Semi-discrete approximations for stochastic differential equations and applications, International Journal of Computer Mathematics, 89(6), to reproduce qualitative properties of a class of nonlinear stochastic differential equations with nonnegative, non-globally Lipschitz coefficients and a unique equilibrium solution. The proposed fixed-time step method preserves the positivity of solutions and reproduces the almost sure asymptotic stability behavior of the equilibrium with no time-step restrictions.
Cite
@article{arxiv.1708.07857,
title = {A note on pathwise stability and positivity of nonlinear stochastic differential equations},
author = {Ioannis S. Stamatiou},
journal= {arXiv preprint arXiv:1708.07857},
year = {2017}
}
Comments
8 pages, 3 figures