Geodesic
Stability of numerical methods for ordinary stochastic differential equations along Lyapunov-type and other functions with variable step sizes
Electronic transactions on numerical analysis, Tome 20 (2005), pp. 27-49.

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Summary: Some general concepts and theorems on the stability of numerical methods for ordinary stochastic differential equations (SDEs) along Lyapunov-type and other Borel-measurable, nonnegative functions are presented.
Classification : 65C20, 65C30, 65C50, 60H10, 37H10, 34F05
Keywords: stochastic-numerical approximation, stochastic stability, ordinary stochastic differential equations, numerical methods, drift-implicit Euler methods, balanced implicit methods, Lyapunov-type functions, numerical weak -stability, stability of moments, a 
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     author = {Schurz, Henri},
     title = {Stability of numerical methods for ordinary stochastic differential equations along {Lyapunov-type} and other functions with variable step sizes},
     journal = {Electronic transactions on numerical analysis},
     pages = {27--49},
     publisher = {mathdoc},
     volume = {20},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2005__20__a14/}
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Schurz, Henri. Stability of numerical methods for ordinary stochastic differential equations along Lyapunov-type and other functions with variable step sizes. Electronic transactions on numerical analysis, Tome 20 (2005), pp. 27-49. http://geodesic.mathdoc.fr/item/ETNA_2005__20__a14/