Applied Lyapunov Stability for Some Nonlinear Stochastic Differential Equations
DOI:
https://doi.org/10.25130/tjps.v28i5.1586Keywords:
stability, stochastic(random) differential equation, the Lyapunov function.Abstract
In this paper, we applied and explain the stability to some linear and non-linear stochastic differential equations by using the Lyapunov direct second method, after finding the stochastic differential equation which obtained by applying the (Ito-integrated formula) and the quadratic Lyapunov function be taken, we use the Lyapunov theorems to find and explain if the trivial (zero) solution are stochastically stabile (p-stable, mean square stable and stochastically asymptotically stable in the large ), then we explain the methods by some examples.
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