You obviously haven't provided info on the circuit your transistor sits in ( which would certainly help ), the frequency, voltage, current, the type of your transistor.... etc.
The on and off times may differ due to technological assymetries, quantum effects and mobility of majority charges. Of course this is not the case here as those values shouldn't differ by more than at most half order of magnitude.
In your case it is quite likely that there is some kind of integrating circuit either on the input or output of your transistor.
I'd rather not suspect the transistor itself because the shape of the falling slope suggests integration, and there are no big capacitances inside the planar structure of the transistor to cause such an effect.
Check your circuit and give more details.
regards, yego