IMM technical report 18/97:
A survey of Lyapunov techniques for stochastic differential equations
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Abstract
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.
IMM publications list
Last modified October 9, 1997
For further information, please contact, Finn Kuno
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