Martingale

In the theory of stochastic processes, a subdiscipline of probability theory, filtrations are totally ordered collections of subsets that are used to model the information that is available at a given point and therefore play an important role in the formalization of random processes.

Sound like the Bayesian model, without replacement. The factorial. What information is available?  The path forward the leads to the least deviation. 

This comes up in Ito's calculus.  If you Bayesian subsets are complete then one can do integrals on many random process.  A Markov 3-Tuple color operator is a finite variation. The Hamiltonian is a square integrable function. The Martingale sequence is the current deviation level.  This means ratios work between color layers, they have been binomial balanced by relative under sampling while maintaining deviation maximum.

The three colors can be treated as Gaussian arrivals within some error band. They can be treated as occupying a fixed bandwidth channel.  If we satisfy this condition then we can be flattened to flat earth with subdivisible  time. In Brownian Motion we can see that Einstein treated the solvent fluid as infinitely divisible, but square integrable fluid.  Ito says that units of time have to count according to order in the subsets. We have partition the integral sum by subset.

But we are finite without time and a flat Lie paper, we are a slightly salad bowl Lie paper.  All the finite sets remain.  Ito wants to know if we have a sufficient flat mesh when we map from the curved model. Markov condition restated

Simpler rule:

The deviations must be set below M in M-1 steps where M is the Markov m-Tuple tree. 

This is also the under sampling process. Adapted means serialization of interactions, so relaxation is never accurate in a semi-martingale, and it is about the finite set of deviations, M, and precision is 1/M.

Ito is another great hero of the theory of everything.  Economists need to think about his conditions, are the paths forward separable and limited in variance?  So in labor, capital, and output, they can be independent arrivals.  Those three sets must be mostly aligned.  Labor subset are small, firm hierarchy less than four.   Estimate capital purchases as best you can from a finite past.  Find the Markov 3-Tuple for labor and capital as x,y,z.  z represents the accuracy of sales, you have  sales to this accuracy.  This is very hard to do.  

This whole theory is about finite sums, adjusting the grid pattern so we minimize sums but keep grid measurements within a bound. The grids get integer spacing, we get a kintetic energy component for round off error, N uncertainty.  A fundamental in self sampled systems.

In finite system n-Tuple there is a point where separability is lost, the triple generates more kinetic energy. Past Avogadro for three small relative primes.  Then the grid in flat units of time increase in fuzzy.  There is an absolute limit to the way three small relative primes can combine and remain separable. Markov is no making an assumption about relative sample rates.  Past the Bayesian Avogadro exponent, I suspect color operators will deviation from finite, bound error, except if we include negative points I guess.