Track state of time series event in SQL column

This seems really simple but I can’t figure it out, working in SQL Server. I have time series data and I want a column to track the state of ON/OFF events for each row, so when there’s an ON event then the Desired Output column will have a 1 for each subsequent event until there is an OFF event. Please see example below. Thanks so much!

TimeStamp	Event	Desired Output
1:01	ON	1
1:02	OFF	0
1:04	other	0
1:05	other	0
1:06	ON	1
1:10	other	1
1:12	other	1
1:14	OFF	0
1:15	other	0

Answer

WITH
  flagged AS
(
  SELECT
    timestamp,
    CASE WHEN event = 'ON'  THEN 1
         WHEN event = 'OFF' THEN 0 END   AS state
  FROM
    #table
),
  cumulative AS
(
  SELECT
    *,
    COUNT(state) OVER (ORDER BY timestamp)   AS state_group
  FROM
    flagged
)
SELECT
  timestamp,
  MAX(state) OVER (PARTITION BY state_group)   AS persisted_state
FROM
  cumulative