Organodynamics

Grant Holland, Apr 25, 2014

Slide: Organodynamic Dependent Stochastic Processes (ODSP)

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An organodynamic dependent stochastic process (ODSP) is an organodynamic stochastic process (OSP) with a twist:

 

Each time step is represented by a joint distribution, rather than a simple distribution.

 

The purpose of using joint distributions at every time step is to take into account any stochastic dependency that may be at work within the process.

 

Often, conditional distributions are used instead. The matrix representation is called a  transition matrix .

 

Information theory provides a number of entropic functionals that are useful in characterizing the degree of chance variation as well as the degree of stochastic dependency of ODSPs:

 

á      Joint entropy H(X,Y)

á      Conditional entropy H(Y|X)

á      Relative entropy D( X || Y)

á      Mutual information I(X;Y)

á      Entropy rate

 

The ODSP takes the place of the Òequations of motionÓ, and forms the principle dynamic construct in organodynamics.

 

 

If the Markov condition holds, then an Organodynamic Markov Chain (OMC) is an ODSP, all of whose transition matrices are the same Markov matrix.




Because stochastic dependence is prominently modeled by ODSPs, the ODSP and the OMC are the principle foundational mathematical constructs of organodynamics.

 

 

Notes: