Couple of questions:
Do your stairs have carpet on them
Is there a handrail, what's it made of
Does the sensor have to concealed, small, temporary or permenant
Wires or radio linked to alarm
Sensor circuits:
Optical break beam,Pressure pad switch,Capacitve,Vibration,
Pyrolectric (Infra red motion) Often found on security floodlights :wink:
Ultrasonic - Doppler shift (motion) and rangefinding (proximity)
Radar - see above, Motion detection only needs a couple of simple ic's but rangefinding is a bit more complex. That and the cavities are a bit expensive and an overkill for domestic use.