arXiv:1708.07857 Abstract | arXiv Analytics

arXiv:1708.07857 [math.NA]Abstract References Reviews Resources

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

Published 2017-08-25Version 1

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.

Comments: 8 pages, 3 figures

Categories: math.NA

Subjects: 60H10, 60H35, 65C20, 65C30, 65J15, 65L20

Keywords: nonlinear stochastic differential equations, pathwise stability, positivity, sure asymptotic stability behavior, fixed-time step method preserves

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