In　this　paper,　we　intend　to　investigate　uniform　global　asymptotic　stability　in　probability　(UGAS-P)　for　a　class　of　time-varying　switched　stochastic　nonlinear　systems.　Conventional　criteria　on　stability　for　switched　stochastic　systems　are　based　on　the　negativity　of　the　infinitesimal　generator　of　Lyapunov　functions,　it　is　demonstrated　that　these　criteria　are　conservative.　Taking　this　fact　into　account,　the　infinitesimal　generator　for　each　active　subsystem　acting　on　Lyapunov　functions　is　relaxed　to　be　indefinite　with　the　help　of　uniformly　stable　function　(USF).　Subsequently,　improved　criteria　on　asymptotic　stability　are　proposed　by　applying　the　weakened　condition　and　mode-dependent　average　dwell　time　(MDADT)　technique.　In　addition,　numerical　examples　are　presented　to　verify　the　effectiveness　of　the　obtained　results.