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Volume 2, Issue 3
On Global Asymptotic Stability of Solutions of Some in-Arithmetic-Mean-Sense Monotone Stochastic Difference Equations in $\rm{IR}^1$

A. Rodkina & H. Schurz

DOI: 10.4208/aamm.09-m0980

Int. J. Numer. Anal. Mod., 2 (2005), pp. 355-366.

Published online: 2005-02

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  • Abstract

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.

  • Keywords

stochastic difference equations, global asymptotic stability, almost sure stability, stochastic differential equations, and partially drift-implicit numerical methods.

  • AMS Subject Headings

39A10, 39A11, 37H10, 60H10, 65C30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-2-355, author = {A. Rodkina and H. Schurz}, title = {On Global Asymptotic Stability of Solutions of Some in-Arithmetic-Mean-Sense Monotone Stochastic Difference Equations in $\rm{IR}^1$}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2005}, volume = {2}, number = {3}, pages = {355--366}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/aamm.09-m0980}, url = {http://global-sci.org/intro/article_detail/ijnam/936.html} }
TY - JOUR T1 - On Global Asymptotic Stability of Solutions of Some in-Arithmetic-Mean-Sense Monotone Stochastic Difference Equations in $\rm{IR}^1$ AU - A. Rodkina & H. Schurz 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 -

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.

A. Rodkina and H. Schurz. (2005). On Global Asymptotic Stability of Solutions of Some in-Arithmetic-Mean-Sense Monotone Stochastic Difference Equations in $\rm{IR}^1$. International Journal of Numerical Analysis and Modeling. 2 (3). 355-366. doi:10.4208/aamm.09-m0980
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