Does strong Markov property impley Markov property?

comtech · science forum Guru Wannabe Joined: 08 Oct 2005 Posts: 150

Dear all,

I understand that Markov property does not imply strong markov
property; but strong markov property implies markov property.

Is my understanding correct?

Thanks a lot!

BuddhaThu · science forum beginner Joined: 06 Oct 2005 Posts: 21

Dear Comtech,

I am not an expert in Markov, but let me take a crack at this.

In interpreting time, you can see it as either discrete or continuous.

This might be the same for interpreting Markov.

There are two types of Markov.

The first type is discrete Markov where you can definitively demarcate
between the past, present and future. It is sort like Monday, Tuesday
and Wednesday with Monday not considered as having causal relation to
Tuesday and Wednesday.

Note: The past is not deleted. It is just not considered into the
relationship.

This might be considered as strong Markov.

The other type is a continuous Markov chain. Here, since it is
continuous, you can only approximate the time difference between the
causal/statistical chain of present to future, with the approximate
past sliced off and not considered.

Note: There is no definitively or objective way to cut the past. There
is only direction and magnitude using vectors.

It is like the Dedekind cut where the cut is created by the
mathematician.

In my interpretation, since it is 'continuous,' there is no real
'cut' at all from the past, even if it is by the **subjective**
hand of the mathematician. This is very different from the discrete
Markov chain.

With the continuous chain, you can only approximate it as the immediate
past and arbitrarily mark it off not to be considered. The past will
always there no matter how minute you cut.

No one can 'cut' an infinite continuum. There is no precise
'cut.'

Hence, the Markov property does not imply strong Markov, while strong
Markov will imply the Markov property.

The strong is a discrete form of the Markov property so that there can
be a 'precision' discrete cut.

The property alone only has the continuous and can only approximate the
cut from the past.

B.T.

C6L1V@shaw.ca · science forum Guru Joined: 23 May 2005 Posts: 628

comtech wrote:

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