TY - JOUR
T1 - On Global Asymptotic Stability of Solutions of Some in-Arithmetic-Mean-Sense Monotone Stochastic Difference Equations in $\rm{IR}^1$
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 355
EP - 366
PY - 2005
DA - 2005/02
SN - 2
DO - http://doi.org/10.4208/aamm.09-m0980
UR - https://global-sci.org/intro/article_detail/ijnam/936.html
KW - stochastic difference equations, global asymptotic stability, almost sure stability, stochastic differential equations, and partially drift-implicit numerical methods.
AB - <p style="text-align: justify;">Global almost sure asymptotic stability of the trivial
solution of some nonlinear stochastic difference equations
with in-the-arithmetic-mean-sense monotone drift part and diffusive part
driven by independent (but not necessarily identically distributed)
random variables is proven under appropriate conditions in $\rm{IR}^1$. This
result can be used to verify asymptotic stability of
stochastic-numerical methods such as partially drift-implicit
trapezoidal methods for nonlinear stochastic differential equations with
variable step sizes.</p>