I'm not aware of an article that covers the math. I think it would be challenging to write a formula for the output voltage, but the frequency of oscillation or duty cycle might be more approachable. Still not trivial, but would be interesting to try.
I've had some success simulating the circuit in LTspice. You need a good model for the 555. It needs to be a CMOS 555. The TTL versions will affect performance or may not work at all. And some 555 models are junk and will never work. My advice would be to walk through the circuit node by node and try to use the node voltages and currents to debug what is not working. If you just look at the output voltage, it will be hard since that isn't telling you much about what's wrong.
It would also be helpful if you have the real circuit built up on the bench so that you can look at the node waveforms with a scope and compare them to the simulation. Beware of the scope probes loading the circuit, particularly the high voltage output. You may need to use a very high impedance probe (or build one) to accurately measure the output voltage.
I'm not sure if you have a kit, but if not I'd recommend purchasing one so that you have a known good set of parts on hand.http://mightyohm.com/blog/products/geiger-counter/