[Bidagdha_TADIR]

Is there a mathematical relationship between the intensity of the light coming to the PMT and the current produced, if so what is it?

[Enthalpy]

A dark current, badly reproducible and depending on the ambient radioactivity, the cosmic rays, the temperature.
Then a photocurrent which is proportional to the incoming light if not too strong.
The multiplication factor depends on the voltage.

You could check photomultiplier datasheets; Hamamatsu sells some.

[Illuminatus]

Photomultiplier data sheets are the more practical approach in-lab, but if you're looking into the theory and want to see what the idealized mathematical relationship is, check out this resource:

http://www2.pv.infn.it/~debari/doc/Flyckt_Marmonier.pdf

I believe the current amplification mathematics start at the very beginning.

Enjoy

[Bidagdha_TADIR]

Checking the reference, thank you.