Second order models

Here’s a real research problem that I’m trying to think about:

How to introduce and study second order models (say for stochastic processes and financial time series) ?

By second order, I mean stochastic difference or diffenrential equations of second order (as opposed to 1st order used in existing literature).

Why 2nd order ?

The hint is taken from physics, where  phase spaces have double the dimension of corresponding configuration spaces.

If one considers only 1st order equations, then one miss out half of the dimensions, and artificially creates too much randomness.

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