A note on pathwise stability and positivity of nonlinear stochastic differential equations

Ioannis S. Stamatiou

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arXiv · 1708.07857

A note on pathwise stability and positivity of nonlinear stochastic differential equations

Ioannis S. Stamatiou

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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.

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Ioannis S. Stamatiou. 2017-08-25. A note on pathwise stability and positivity of nonlinear stochastic differential equations. https://arxiv.org/abs/1708.07857

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