Dissipative stochastic differential equations are mean-square dissipative, and their stability and bifurcations can be analyzed via linearised systems using deterministic methods.
Adaptive time-stepping strategies for nonlinear stochas- tic systems
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Mean-square Stability and Bifurcations for Dissipative SDEs
Dissipative stochastic differential equations are mean-square dissipative, and their stability and bifurcations can be analyzed via linearised systems using deterministic methods.