IMM technical report 18/97:

A survey of Lyapunov techniques for stochastic differential equations

Uffe H. Thygesen

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This note reviews Lyapunov-like theorems addressing qualitative properties of solutions to stochastic differential equations (in the sense of Ito). The qualitative properties we address are regularity, stochastic boundedness, stochastic stability, stability of moments as well as existence and properties of stationary solutions. We review the existing Lyapunov-like theorems which give conditions for a system to possess these properties; the conditions are given in terms of the existence of a auxiliary (Lyapunov) function.

We illustrate the theory with two examples and finally we point out some areas of current research within the field of stochastic Lyapunov theory.

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Last modified October 9, 1997

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