A Stochastic Jurdjevic--Quinn Theorem

The purpose of this paper is to state sufficient conditions for the stabilizability of stochastic differential systems when both the drift and diffusion terms are affine in the control. This result extends to stochastic differential systems the well-known theorem of Jurdjevic--Quinn [J. Differential Equations, 28 (1978), pp. 381--389] and incorporates earlier stabilization results proved in [P. Florchinger, Stochastic Anal. Appl., 12 (1994), pp. 473--480] and [R. Chabour and M. Oumoun, Stochastic Anal. Appl., 16 (1998), pp. 43--50].