Abstract
This paper investigates the boundedness conditions of solutions of stochastic differential equations in the almost sure sense. Boundedness is one of the most fundamental properties in a lot of control problems. In general, it is hard to investigate almost sure boundedness of solutions of stochastic differential equations, unlike deterministic systems. However, for a class of systems, the almost sure boundedness can be investigated. This paper deals with conditions for the almost sure boundedness of stochastic systems, which is based on boundary properties of one-dimensional diffusion processes. Moreover, based on the boundedness, we show the characterization of a kind of practical asymptotic stability of one-dimensional stochastic systems in the almost sure sense. The presented results are validated through a numerical example.
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