The Cooling and Diffusion Equations

日期:2014/03/07

First order differential equations of the form:

the rate of change of a variable + the original variable x a constant equals a constant times a function, or

dy/dt + p * y =  k1 * q(t)

has wide applicability in all physical settings. it's used to model the cooling and diffusion equations for example,  as Arthur Mattuck in a brilliant and relatively easy to assimilate lecture shows.



For what variable in the market does its rate of change depend on its level and the movements of a second variable. The moves of stocks relative to bonds and currencies comes to mind. Is it predictive in certain cases and how do random perturbations affect the solution and its predictivity ? Are there any methods used to solve these first order equations that are useful for markets without regard to stochastic, useless solutions?