In probability theory, a stochastic process, or sometimes random process, is the counterpart to a deterministic process (or deterministic system). Instead of dealing with only one possible reality of how the process might evolve under time (as is the case, for example, for solutions of an ordinary differential equation), in a stochastic or random process there is some indeterminacy in its future evolution described by probability distributions. This means that even if the initial condition (or starting point) is known, there are many possibilities the process might go to, but some paths may be more probable and others less so.
.... Manufacturing processes are assumed to be stochastic processes. This assumption is largely valid for either continuous or batch manufacturing processes. Testing and monitoring of the process is recorded using a process control chart which plots a given process control parameter over time. Typically a dozen or many more parameters will be tracked simultaneously. Statistical models are used to define limit lines which define when corrective actions must be taken to bring the process back to its intended operational window.
I think this may get at some of the issues that bedevil the debate. I think I'd understand consciousness to be a stochastic process. There are physical elements moving around, which in sum equal thought. But because we don't have good enough data on every particle, or even a precise understanding of how groups of particles actually represent thought, we can't comfortably call anything explicitly deterministic.
Yet, as with manufacturing processes, we do have a sense of probability parameters. We do know that if we tweak one or another parameter, the outcomes will change. I think it is this vagueness which fools people into believing that the brain is not ultimately determined. Yet there is a difference between a determined system and determinism. The batch of cookies is not a determined system - in the sense that each cookie will turn out slightly different. But the physical properties underlying how cookies bake is entirely deterministic.