Wednesday, October 30, 2013
Stochastic Drift And The Central Limit Theorem
I've been going through some books on stochastic processes such as Gillespie's Markov Processes and Kittel's Elementary Statistical Physics. The two characterizing functions of a continuous Markov process are the drift function and the diffusion function. These seem to be the analogs of what I have called "signal" and "noise" in the preceding blogs. It may be that the Earth's equilibrium temperatures are subject to drift over time which would be difficult to distinguish from global warming. If a drift is persistent it will have consequences over time but would not be as serious as a run-away greenhouse effect.
Global warming does not appear to be a well studied as a stochastic process. Maxwell, Boltzmann and Gibbs introduced the concepts of statistical physics to the study of gases and Einstein's explanation of Brownian motion extended this to liquids. The Earth can be considered as a physical system in contact with an external heat source and it is normal for there to be fluctuations in temperature but I doubt that we need a Lyapunov control system to clamp the Earth's mean temperature to some arbitrarily chosen fixed value.
The weighted sum of normal distribution functions that was found to be a good fit for the variation in the monthly global land anomaly may have a variation of the Lyapunov central limit theorem associated with it but it's definitely not a normal distribution.